Zhilin Li

Chai, S., Li, Z., Zhang, Z., & Zhang, Z. (2024). A pressure Poisson equation-based second-order method for solving two-dimensional moving contact line problems with topological changes. COMPUTERS & FLUIDS, 269. https://doi.org/10.1016/j.compfluid.2023.106117

Li, Z., & Pan, K. (2024, July). Coupled transformation methods and analysis for BVPs on infinite domains. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, Vol. 444. https://doi.org/10.1016/j.cam.2024.115771

Ye, Z., Zheng, Z., & Li, Z. (2024, February 28). New third-order convex splitting methods and analysis for the phase field crystal equation. NUMERICAL ALGORITHMS, Vol. 2. https://doi.org/10.1007/s11075-024-01782-3

Pan, K., Wu, X., Hu, H., & Li, Z. (2023, December 14). A CELL-CENTERED MULTIGRID SOLVER FOR THE FINITE VOLUME DISCRETIZATION OF ANISOTROPIC ELLIPTIC INTERFACE PROBLEMS ON IRREGULAR DOMAINS*. JOURNAL OF COMPUTATIONAL MATHEMATICS, Vol. 12. https://doi.org/10.4208/jcm.2308-m2023-0029

Dong, B., Li, Z., & Ruiz-Alvarez, J. (2023, July 10). A Stable FE-FD Method for Anisotropic Parabolic PDEs with Moving Interfaces. COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION, Vol. 7. https://doi.org/10.1007/s42967-023-00281-x

Li, J., Li, Z., & Pan, K. (2023). Accurate derivatives approximations and applications to some elliptic PDEs using HOC methods. APPLIED MATHEMATICS AND COMPUTATION, 459. https://doi.org/10.1016/j.amc.2023.128265

Amat, S., Li, Z., Ruiz-Alvarez, J., Solano, C., & Trillo, J. C. (2023). Adapting Cubic Hermite Splines to the Presence of Singularities Through Correction Terms. JOURNAL OF SCIENTIFIC COMPUTING, 95(3). https://doi.org/10.1007/s10915-023-02191-9

Hu, S., Pan, K., Wu, X., Ge, Y., & Li, Z. (2023). An efficient extrapolation multigrid method based on a HOC scheme on nonuniform rectilinear grids for solving 3D anisotropic convection-diffusion problems. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 403. https://doi.org/10.1016/j.cma.2022.115724

Ji, H., Wang, F., Chen, J., & Li, Z. (2023). Analysis of nonconforming IFE methods and a new scheme for elliptic interface problems. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 57(4), 2041–2076. https://doi.org/10.1051/m2an/2023047

Li, Z., & Pan, K. (2023). HIGH ORDER COMPACT SCHEMES FOR FLUX TYPE BCS. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 45(2), A646–A674. https://doi.org/10.1137/21M1444771

Dong, B., Li, Z., & Ruiz-Álvarez, J. (2023). Higher Order Finite Element Methods for Some One-dimensional Boundary Value Problems. Research Reports on Computer Science, 2(1), 15–27. https://doi.org/10.37256/rrcs.212023

Dong, B., Li, Z., & Ruiz-Álvarez, J. (2023). Higher Order Finite Element Methods for Some One-dimensional Boundary Value Problems. Research Reports on Computer Science. https://doi.org/10.37256/rrcs.2120232118

Pan, K., Fu, K., Li, J., Hu, H., & Li, Z. (2023). New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 16(2), 393–409. https://doi.org/10.4208/nmtma.OA-2022-0073

Li, Z., & Mikayelyan, H. (2023). Numerical analysis of a free boundary problem with non-local obstacles. APPLIED MATHEMATICS LETTERS, 135. https://doi.org/10.1016/j.aml.2022.108414

Amat, S., Li, Z., Ruiz-Alvarez, J., Solano, C., & Trillo, J. C. (2023). Numerical integration rules with improved accuracy close to discontinuities. MATHEMATICS AND COMPUTERS IN SIMULATION, 210, 593–614. https://doi.org/10.1016/j.matcom.2023.03.032

Li, Z., Pan, K., & Ruiz-Alvarez, J. (2023, November 6). Stable high order FD methods for interface and internal layer problems based on non-matching grids. NUMERICAL ALGORITHMS, Vol. 11. https://doi.org/10.1007/s11075-023-01680-0

Li, R., Yin, J.-F., & Li, Z.-L. (2022, February 16). A Variant Modified Skew-Normal Splitting Iterative Method for Non-Hermitian Positive Definite Linear Systems. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, Vol. 2. https://doi.org/10.4208/nmtma.OA-2021-0038

Pan, K., Wu, X., Hu, H., Yu, Y., & Li, Z. (2022). A new FV scheme and fast cell-centered multigrid solver for 3D anisotropic diffusion equations with discontinuous coefficients. JOURNAL OF COMPUTATIONAL PHYSICS, 449. https://doi.org/10.1016/j.jcp.2021.110794

Ji, H., Wang, F., Chen, J., & Li, Z. (2022). A new parameter free partially penalized immersed finite element and the optimal convergence analysis. NUMERISCHE MATHEMATIK, 150(4), 1035–1086. https://doi.org/10.1007/s00211-022-01276-1

Singh, S., Singh, S., & Li, Z. (2022). A new patch up technique for elliptic partial differential equation with irregularities. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 407. https://doi.org/10.1016/j.cam.2021.113975

Dong, B., Feng, X., & Li, Z. (2022). AN L-8 SECOND ORDER CARTESIAN METHOD FOR 3D ANISOTROPIC INTERFACE PROBLEMS. JOURNAL OF COMPUTATIONAL MATHEMATICS, 40(6), 882–912. https://doi.org/10.4208/jcm.2103-m2020-0107

Ji, H., Wang, F., Chen, J., & Li, Z. (2022). An immersed C R-P-0 element for Stokes interface problems and the optimal convergence analysis. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 399. https://doi.org/10.1016/j.cma.2022.115306

Pan, K., He, D., & Li, Z. (2021). A High Order Compact FD Framework for Elliptic BVPs Involving Singular Sources, Interfaces, and Irregular Domains. JOURNAL OF SCIENTIFIC COMPUTING, 88(3). https://doi.org/10.1007/s10915-021-01570-4

Li, R., Li, Z.-L., & Yin, J.-F. (2021, June 3). A generalized modulus-based Newton method for solving a class of non-linear complementarity problems with P-matrices. NUMERICAL ALGORITHMS, Vol. 6. https://doi.org/10.1007/s11075-021-01136-3

Zhang, C., Li, Z., & Yue, X. (2021). Acceleration Technique for the Augmented IIM for 3D Elliptic Interface Problems. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 14(3), 773–796. https://doi.org/10.4208/nmtma.OA-2020-0112

Deng, S., Li, Z., & Pan, K. (2021). An ADI-Yee's scheme for Maxwell's equations with discontinuous coefficients. JOURNAL OF COMPUTATIONAL PHYSICS, 438. https://doi.org/10.1016/j.jcp.2021.110356

Li, Z., & Norris, L. (2021). An Introduction to Partial Differential Equations (with Maple). https://doi.org/10.1142/12052

Tong, F., Feng, X., & Li, Z. (2021). Fourth order compact FD methods for convection diffusion equations with variable coefficients. APPLIED MATHEMATICS LETTERS, 121. https://doi.org/10.1016/j.aml.2021.107413

Jiang, H., Yang, Z., & Li, Z. (2021). Non-parallel hyperplanes ordinal regression machine. KNOWLEDGE-BASED SYSTEMS, 216. https://doi.org/10.1016/j.knosys.2020.106593

Xu, J., Su, H., & Li, Z. (2021, November 13). Optimal convergence of three iterative methods based on nonconforming finite element discretization for 2D/3D MHD equations. NUMERICAL ALGORITHMS, Vol. 11. https://doi.org/10.1007/s11075-021-01224-4

Huang, P., & Li, Z. (2021). Partially penalized IFE methods and convergence analysis for elasticity interface problems. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 382. https://doi.org/10.1016/j.cam.2020.113059

Partially penalized IFE methods and convergence analysis for elasticity interface problems. (2021). Journal of Computational and Applied Mathematics.

Ye, J., Yang, Z., & Li, Z. (2021). Quadratic hyper-surface kernel-free least squares support vector regression. INTELLIGENT DATA ANALYSIS, 25(2), 265–281. https://doi.org/10.3233/IDA-205094

Xiao, X., Feng, X., & Li, Z. (2021). The local tangential lifting method for moving interface problems on surfaces with applications. JOURNAL OF COMPUTATIONAL PHYSICS, 431. https://doi.org/10.1016/j.jcp.2021.110146

Dong, B., Feng, X., & Li, Z. (2020). AN FE-FD METHOD FOR ANISOTROPIC ELLIPTIC INTERFACE PROBLEMS. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 42(4), B1041–B1066. https://doi.org/10.1137/19M1291030

Tong, F., Wang, W., Feng, X., Zhao, J., & Li, Z. (2020). How to obtain an accurate gradient for interface problems? Journal of Computational Physics, 405, 109070. https://doi.org/10.1016/j.jcp.2019.109070

Chen, X., Feng, X., & Li, Z. (2019). A direct method for accurate solution and gradient computations for elliptic interface problems. NUMERICAL ALGORITHMS, 80(3), 709–740. https://doi.org/10.1007/s11075-018-0503-5

Xiao, X., Feng, X., & Li, Z. (2019). A gradient recovery-based adaptive finite element method for convection-diffusion-reaction equations on surfaces. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 120(7), 901–917. https://doi.org/10.1002/nme.6163

Li, Z., Dong, B., Tong, F., & Wang, W. (2019). An Augmented IB Method & Analysis for Elliptic BVP on Irregular Domains. CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 119(1), 63–72. https://doi.org/10.32604/cmes.2019.04635

Yao, Y., Zhang, Y., Tian, L., Zhou, N., Li, Z., & Wang, M. (2019). Analysis of Network Structure of Urban Bike-Sharing System: A Case Study Based on Real-Time Data of a Public Bicycle System. SUSTAINABILITY, 11(19). https://doi.org/10.3390/su11195425

Zhao, T., Zhang, J., Li, Z., & Zhang, Z. (2019). Numerical Validations of the Tangent Linear Model for the Lorenz Equations. CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 120(1), 83–104. https://doi.org/10.32604/cmes.2019.04483

Yao, Y., Jiang, X., & Li, Z. (2019). Spatiotemporal characteristics of green travel: A classification study on a public bicycle system. JOURNAL OF CLEANER PRODUCTION, 238. https://doi.org/10.1016/j.jclepro.2019.117892

Chen, X., Li, Z., & Ruiz Alvarez, J. (2018). A direct IIM approach for two-phase Stokes equations with discontinuous viscosity on staggered grids. COMPUTERS & FLUIDS, 172, 549–563. https://doi.org/10.1016/j.compfluid.2018.03.038

Ji, H., Chen, J., & Li, Z. (2018). A high-order source removal finite element method for a class of elliptic interface problems. APPLIED NUMERICAL MATHEMATICS, 130, 112–130. https://doi.org/10.1016/j.apnum.2018.03.017

Li, Z., Lai, M.-C., Peng, X., & Zhang, Z. (2018). A least squares augmented immersed interface method for solving Navier-Stokes and Darcy coupling equations. COMPUTERS & FLUIDS, 167, 384–399. https://doi.org/10.1016/j.compfluid.2018.03.032

Hu, R., & Li, Z. (2018). Error analysis of the immersed interface method for Stokes equations with an interface. APPLIED MATHEMATICS LETTERS, 83, 207–211. https://doi.org/10.1016/j.aml.2018.03.034

Li, Z., Zhonghua, Q., & Tang, T. (2018). Numerical solution of differential equations: Introduction to finite difference and finite element methods. New York: Cambridge University Press.

Li, Z., Chen, X., & Zhang, Z. (2018). ON MULTISCALE ADI METHODS FOR PARABOLIC PDEs WITH A DISCONTINUOUS COEFFICIENT. MULTISCALE MODELING & SIMULATION, 16(4), 1623–1647. https://doi.org/10.1137/17M1151985

Qin, F., Chen, J., Li, Z., & Cai, M. (2017). A Cartesian grid nonconforming immersed finite element method for planar elasticity interface problems. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 73(3), 404–418. https://doi.org/10.1016/j.camwa.2016.11.033

Huang, P., & Li, Z. (2017). A Uniformly Stable Nonconforming FEM Based on Weighted Interior Penalties for Darcy-Stokes-Brinkman Equations. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 10(1), 22–43. https://doi.org/10.4208/nmtma.2017.m1610

Qin, F., Wang, Z., Ma, Z., & Li, Z. (2017). ACCURATE GRADIENT COMPUTATIONS AT INTERFACES USING FINITE ELEMENT METHODS. INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE, 27(3), 527–537. https://doi.org/10.1515/amcs-2017-0037

Li, Z., Ji, H., & Chen, X. (2017). ACCURATE SOLUTION AND GRADIENT COMPUTATION FOR ELLIPTIC INTERFACE PROBLEMS WITH VARIABLE COEFFICIENTS. SIAM JOURNAL ON NUMERICAL ANALYSIS, 55(2), 570–597. https://doi.org/10.1137/15m1040244

Li, Z., & Qin, F. (2017). An Augmented Method for 4th Order PDEs with Discontinuous Coefficients. JOURNAL OF SCIENTIFIC COMPUTING, 73(2-3), 968–979. https://doi.org/10.1007/s10915-017-0487-7

Angot, P., & Li, Z. L. (2017). An augmented IIM & preconditioning technique for jump embedded boundary conditions. International Journal of Numerical Analysis and Modeling, 14(4-5), 712–729.

Yan, J., Lai, M.-C., Li, Z., & Zhang, Z. (2017). New Conservative Finite Volume Element Schemes for the Modified Regularized Long Wave Equation. ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 9(2), 250–271. https://doi.org/10.4208/aamm.2014.m888

Li, Z., Qiao, Z., & Tang, T. (2017). Numerical Solution of Differential Equations. In Cambridge University Press. https://doi.org/10.1017/9781316678725

Amat, S., Li, Z., & Ruiz, J. (2017). On an New Algorithm for Function Approximation with Full Accuracy in the Presence of Discontinuities Based on the Immersed Interface Method. Journal of Scientific Computing, 75(3), 1500–1534. https://doi.org/10.1007/S10915-017-0596-3

Zhang, Q., Li, Z., & Zhang, Z. (2016). A Sparse Grid Stochastic Collocation Method for Elliptic Interface Problems with Random Input. JOURNAL OF SCIENTIFIC COMPUTING, 67(1), 262–280. https://doi.org/10.1007/s10915-015-0080-x

Ji, H., Chen, J., & Li, Z. (2016). A new augmented immersed finite element method without using SVD interpolations. NUMERICAL ALGORITHMS, 71(2), 395–416. https://doi.org/10.1007/s11075-015-9999-0

Li, Z. (2016). An augmented Cartesian grid method for Stokes-Darcy fluid-structure interactions. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 106(7), 556–575. https://doi.org/10.1002/nme.5131

Zhang, S. D. M., & Li, Z. L. (2016). An augmented iim for helmholtz/poisson equations on irregular domains in complex space. International Journal of Numerical Analysis and Modeling, 13(1), 166–178.

Ji, H., Chen, J., & Li, Z. (2016). Augmented immersed finite element methods for some elliptic partial differential equations. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 93(3), 540–558. https://doi.org/10.1080/00207160.2015.1005010

Li, Z., & Mikayelyan, H. (2016). Fine numerical analysis of the crack-tip position for a Mumford-Shah minimizer. INTERFACES AND FREE BOUNDARIES, 18(1), 75–90. https://doi.org/10.4171/ifb/357

Su, X. L., Feng, X. F., & Li, Z. L. (2016). Fourth-order compact schemes for Helmholtz equations with piecewise wave numbers in the polar coordinates. Journal of Computational Mathematics, 34(5), 499–510.

Melnyk, L. J., Wang, Z., Li, Z., & Xue, J. (2016). Prioritization of pesticides based on daily dietary exposure potential as determined from the SHEDS model. FOOD AND CHEMICAL TOXICOLOGY, 96, 167–173. https://doi.org/10.1016/j.fct.2016.07.025

Zhu, L., Zhang, Z. Y., & Li, Z. L. (2016). The immersed finite volume element method for some interface problems with nonhomogeneous jump conditions. International Journal of Numerical Analysis and Modeling, 13(3), 368–382.

Zeng, Y., Chen, J., & Li, Z. (2015). A parallel Robin-Robin domain decomposition method for H(div)-elliptic problems. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 92(2), 394–410. https://doi.org/10.1080/00207160.2014.892587

Li, Z., Xiao, L., Cai, Q., Zhao, H., & Luo, R. (2015). A semi-implicit augmented IIM for Navier-Stokes equations with open, traction, or free boundary conditions. JOURNAL OF COMPUTATIONAL PHYSICS, 297, 182–193. https://doi.org/10.1016/j.jcp.2015.05.003

Zhu, L., Zhang, Z., & Li, Z. (2015). An immersed finite volume element method for 2D PDEs with discontinuous coefficients and non-homogeneous jump conditions. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 70(2), 89–103. https://doi.org/10.1016/j.camwa.2015.04.012

Xia, J., Li, Z., & Ye, X. (2015). Effective matrix-free preconditioning for the augmented immersed interface method. JOURNAL OF COMPUTATIONAL PHYSICS, 303, 295–312. https://doi.org/10.1016/j.jcp.2015.09.050

Zhang, Q., Ito, K., Li, Z., & Zhang, Z. (2015). Immersed finite elements for optimal control problems of elliptic PDEs with interfaces. JOURNAL OF COMPUTATIONAL PHYSICS, 298, 305–319. https://doi.org/10.1016/j.jcp.2015.05.050

Li, Z., Wang, L., Aspinwall, E., Cooper, R., Kuberry, P., Sanders, A., & Zeng, K. (2015). Some new analysis results for a class of interface problems. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 38(18), 4530–4539. https://doi.org/10.1002/mma.2865

Ruiz Alvarez, J., & Li, Z. (2015). The immersed interface method for axis-symmetric problems and application to the Hele-Shaw flow. APPLIED MATHEMATICS AND COMPUTATION, 264, 179–197. https://doi.org/10.1016/j.amc.2015.03.131

Xu, J.-J., Huang, Y., Lai, M.-C., & Li, Z. (2014). A Coupled Immersed Interface and Level Set Method for Three-Dimensional Interfacial Flows with Insoluble Surfactant. COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 15(2), 451–469. https://doi.org/10.4208/cicp.241012.310513a

Ji, H., Chen, J., & Li, Z. (2014). A Symmetric and Consistent Immersed Finite Element Method for Interface Problems. JOURNAL OF SCIENTIFIC COMPUTING, 61(3), 533–557. https://doi.org/10.1007/s10915-014-9837-x

Xiao, L., Cai, Q., Li, Z., Zhao, H., & Luo, R. (2014). A multi-scale method for dynamics simulation in continuum solvent models. I: Finite-difference algorithm for Navier–Stokes equation. Chemical Physics Letters, 616-617, 67–74. https://doi.org/10.1016/J.CPLETT.2014.10.033

Li, Z. (2014). On convergence of the immersed boundary method for elliptic interface problems. Mathematics of Computation, 84(293), 1169–1188. https://doi.org/10.1090/s0025-5718-2014-02932-3

Li, Z. L. (2014). Special issue on fluid structure interactions preface. Numerical Mathematics: Theory, Methods and Applications, 7(4), I-.

Wang, Q., Zhang, Z., & Li, Z. (2013). A Fourier finite volume element method for solving two-dimensional quasi-geostrophic equations on a sphere. APPLIED NUMERICAL MATHEMATICS, 71, 1–13. https://doi.org/10.1016/j.apnum.2013.03.007

Li, Z., & Song, P. (2013). Adaptive mesh refinement techniques for the immersed interface method applied to flow problems. COMPUTERS & STRUCTURES, 122, 249–258. https://doi.org/10.1016/j.compstruc.2013.03.013

Liu, X., Wang, C., Wang, J., Li, Z., Zhao, H., & Luo, R. (2013). Exploring a charge-central strategy in the solution of Poisson's equation for biomolecular applications. PHYSICAL CHEMISTRY CHEMICAL PHYSICS, 15(1), 129–141. https://doi.org/10.1039/c2cp41894k

Wang, C., Wang, J., Cai, Q., Li, Z., Zhao, H.-K., & Luo, R. (2013). Exploring accurate Poisson-Boltzmann methods for biomolecular simulations. COMPUTATIONAL AND THEORETICAL CHEMISTRY, 1024, 34–44. https://doi.org/10.1016/j.comptc.2013.09.021

Botello-Smith, W. M., Liu, X., Cai, Q., Li, Z., Zhao, H., & Luo, R. (2013). Numerical Poisson-Boltzmann model for continuum membrane systems. CHEMICAL PHYSICS LETTERS, 555, 274–281. https://doi.org/10.1016/j.cplett.2012.10.081

Song, P., Xue, J., & Li, Z. (2013). Simulation of Longitudinal Exposure Data with Variance-Covariance Structures Based on Mixed Models. RISK ANALYSIS, 33(3), 469–479. https://doi.org/10.1111/j.1539-6924.2012.01869.x

Hou, S., Li, Z., Wang, L., & Wang, W. (2012). A Numerical Method for Solving Elasticity Equations with Interfaces. COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 12(2), 595–612. https://doi.org/10.4208/cicp.160910.130711s

Ho, J., Li, Z., & Lubkin, S. R. (2012). AN AUGMENTED IMMERSED INTERFACE METHOD FOR MOVING STRUCTURES WITH MASS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 17(4), 1175–1184. https://doi.org/10.3934/dcdsb.2012.17.1175

Li, Z., & Song, P. (2012). An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods. COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 12(2), 515–527. https://doi.org/10.4208/cicp.070211.150811s

Li, Z. (Ed.). (2012). Discrete and Continuous Dynamical Systems, Series B: Mathematical Modeling, Analysis and Computations (Vol. 17) [Special Issue dedicated to Thomas Beale and the FAN conference].

Caraus, I., & Li, Z. (2012). Numerical Solutions of the System of Singular Integro-Differential Equations in Classical Holder Spaces. ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 4(6), 737–750. https://doi.org/10.4208/aamm.12-12s04

Wan, X., & Li, Z. (2012). SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 17(4), 1155–1174. https://doi.org/10.3934/dcdsb.2012.17.1155

SPECIAL ISSUE ON FLUID DYNAMICS, ANALYSIS AND NUMERICS. (2012).

Feng, X., & Li, Z. (2012). Simplified immersed interface methods for elliptic interface problems with straight interfaces. Numerical Methods for Partial Differential Equations, 28(1), 188–203. https://doi.org/10.1002/num.20614

Special Issue on Fluid Motion Driven by Immersed Structures. (2012). In Global Sciences. Retrieved from https://www.researchgate.net/publication/296762774_Special_Issue_on_Fluid_Motion_Driven_by_Immersed_Structures_Preface

Layton, A., Stockie, J., Li, Z. L., & Huang, H. X. (2012). Special issue on fluid motion driven by immersed structures preface. Communications in Computational Physics, 12(2), I-.

Ito, K., Li, Z., & Qiao, Z. (2012). The Sensitivity Analysis for the Flow Past Obstacles Problem with Respect to the Reynolds Number. ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 4(1), 21–35. https://doi.org/10.4208/aamm.11-m1110

Xie, H., Li, Z. L., & Qiao, Z. H. (2011). A finite element method for elasticity interface problems with locally modified triangulations. International Journal of Numerical Analysis and Modeling, 8(2), 189–200.

Wu, C. T., Li, Z. L., & Lai, M. C. (2011). Adaptive mesh refinement for elliptic interface problems using the non-conforming immersed finite element method. International Journal of Numerical Analysis and Modeling, 8(3), 466–483.

Feng, X. F., Li, Z. L., & Qiao, Z. H. (2011). High order compact finite difference schemes for the helmholtz equation with discontinuous coefficients. Journal of Computational Mathematics, 29(3), 324–340.

Xu, J.-J., Li, Z., Lowengrub, J., & Zhao, H. (2011). Numerical Study of Surfactant-Laden Drop-Drop Interactions. COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 10(2), 453–473. https://doi.org/10.4208/cicp.090310.020610a

Ruiz Alvarez, J., Chen, J., & Li, Z. (2011). The IIM in polar coordinates and its application to electro capacitance tomography problems. NUMERICAL ALGORITHMS, 57(3), 405–423. https://doi.org/10.1007/s11075-010-9436-3

Li, Z., Lai, M.-C., He, G., & Zhao, H. (2010). An augmented method for free boundary problems with moving contact lines. COMPUTERS & FLUIDS, 39(6), 1033–1040. https://doi.org/10.1016/j.compfluid.2010.01.013

Gong, Y., & Li, Z. L. (2010). Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions. Numerical Mathematics: Theory, Methods and Applications, 3(1), 23–39.

Yang, X., Zhang, X., Li, Z., & He, G.-W. (2009). A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations. JOURNAL OF COMPUTATIONAL PHYSICS, 228(20), 7821–7836. https://doi.org/10.1016/j.jcp.2009.07.023

Ito, K., Lai, M.-C., & Li, Z. (2009). A well-conditioned augmented system for solving Navier-Stokes equations in irregular domains. JOURNAL OF COMPUTATIONAL PHYSICS, 228(7), 2616–2628. https://doi.org/10.1016/j.jcp.2008.12.028

Wang, J., Cai, Q., Li, Z.-L., Zhao, H.-K., & Luo, R. (2009). Achieving energy conservation in Poisson-Boltzmann molecular dynamics: Accuracy and precision with finite-difference algorithms. CHEMICAL PHYSICS LETTERS, 468(4-6), 112–118. https://doi.org/10.1016/j.cplett.2008.12.049

Wang, F., Chen, J., Xu, W., & Li, Z. (2009). An additive Schwarz preconditioner for the mortar-type rotated Q(1) FEM for elliptic problems with discontinuous coefficients. APPLIED NUMERICAL MATHEMATICS, 59(7), 1657–1667. https://doi.org/10.1016/j.apnum.2008.11.006

Jiang, Q. L., Li, Z. L., & Lubkin, S. R. (2009). Analysis and computation for a fluid mixture model. Communications in Computational Physics, 5(2-4), 620–634.

Khoo, B. C., Li, Z., & Lin, P. (2009). Interface Problems and Methods in Biological and Physical Flows. In B. C. Khoo, Z. Li, & P. Lin (Eds.), WORLD SCIENTIFIC. https://doi.org/10.1142/7147

B. C. Khoo, Z. L., & Lin, P. (Eds.). (2009). Interface problems and methods in biological and physical flows. New Jersey: World Scientific.

Chen, G., Li, Z., & Lin, P. (2008). A fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow. ADVANCES IN COMPUTATIONAL MATHEMATICS, 29(2), 113–133. https://doi.org/10.1007/s10444-007-9043-6

Xie, H., Ito, K., Li, Z., & Toivanen, J. (2008). A finite element method for interface problems with locally modified triangulations. Moving interface problems and applications in fluid dynamics, 466, 179–190. https://doi.org/10.1090/conm/466/09122

Rutka, V., & Li, Z. (2008). An explicit jump immersed interface method for two-phase Navier-Stokes equations with interfaces. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, Vol. 197, pp. 2317–2328. https://doi.org/10.1016/j.cma.2007.12.016

Tan, Z., Le, D. V., Li, Z., Lim, K. M., & Khoo, B. C. (2008). An immersed interface method for solving incompressible viscous flows with piecewise constant viscosity across a moving elastic membrane. JOURNAL OF COMPUTATIONAL PHYSICS, 227(23), 9955–9983. https://doi.org/10.1016/j.jcp.2008.08.013

Gong, Y., Li, B., & Li, Z. (2008). Immersed-interface finite-element methods for elliptic interface problems with nonhomogeneous jump conditions. SIAM JOURNAL ON NUMERICAL ANALYSIS, 46(1), 472–495. https://doi.org/10.1137/060666482

Wan, X., Li, Z., & Lubkin, S. R. (2008). Mechanics of mesenchymal contribution to clefting force in branching morphogenesis. BIOMECHANICS AND MODELING IN MECHANOBIOLOGY, 7(5), 417–426. https://doi.org/10.1007/s10237-007-0105-y

Li, Z., Pao, C. V., & Qiao, Z. (2007). A Finite Difference Method and Analysis for 2D Nonlinear Poisson–Boltzmann Equations. Journal of Scientific Computing, 30(1), 61–81. https://doi.org/10.1007/s10915-005-9019-y

Gremaud, P. A., Kuster, C. M., & Li, Z. (2007). A study of numerical methods for the level set approach. APPLIED NUMERICAL MATHEMATICS, Vol. 57, pp. 837–846. https://doi.org/10.1016/j.apnum.2006.07.022

Li, Z., Ito, K., & Lai, M.-C. (2007). An augmented approach for Stokes equations with a discontinuous viscosity and singular forces. COMPUTERS & FLUIDS, 36(3), 622–635. https://doi.org/10.1016/j.compfluid.2006.03.003

Li, Z., Lubkin, S., & Wan, X. (2007). An augmented immersed interface-level set method for Stokes equations with discontinuous viscosity. Electronic Journal of Differential Equations, Conference, 15, 193–210.

Li, Z., Lai, M.-C., & Ito, K. (2007). An immersed interface method for the Navier-Stokes equations on irregular domains. PAMM, 7(1), 1025401–1025402. https://doi.org/10.1002/pamm.200700758

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Moving Interface Problems and Applications in Fluid Dynamics. (2007). In AMS Contemporary mathematics 466. Retrieved from https://books.google.com/books/about/Moving_Interface_Problems_and_Applicatio.html?id=fMYbCAAAQBAJ

Li, Z., Song, Y., & Tang, T. (2007). Preface of the special issue of APNUM - International Conference on Scientific Computing in Nanjing, China. APPLIED NUMERICAL MATHEMATICS, Vol. 57, pp. 473–474. https://doi.org/10.1016/j.apnum.2006.07.023

Special Issue for the International Conference on Scientific Computing. (2007). Retrieved from https://www.sciencedirect.com/journal/applied-numerical-mathematics/vol/57/issue/5

Xu, J. J., Li, Z. L., Lowengrub, J., & Zhao, H. K. (2006). A level-set method for interfacial flows with surfactant. JOURNAL OF COMPUTATIONAL PHYSICS, 212(2), 590–616. https://doi.org/10.1016/j.jcp.2005.07.016

Li, Z. L., Wan, X. H., Ito, K., & Lubkin, S. R. (2006). An augmented approach for the pressure boundary condition in a Stokes flow. Communications in Computational Physics, 1(5), 874–885.

Li, Z., Qiao, Z.-hua, & Tang, T. (2006). Efficient numerical methods for the 2D nonlinear Poisson–Boltzmann equation modeling charged spheres. Journal of Computational Mathematics, 24(3), 252–264.

Lai, M. C., Li, Z. L., & Lin, X. B. (2006). Fast solvers for 3D Poisson equations involving interfaces in a finite or the infinite domain. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 191(1), 106–125. https://doi.org/10.1016/j.cam.2005.04.025

Ito, K., & Li, Z. L. (2006). Interface conditions for Stokes equations with a discontinuous viscosity and surface sources. APPLIED MATHEMATICS LETTERS, 19(3), 229–234. https://doi.org/10.1016/j.aml.2005.02.041

Li, Z., & Ito, K. (2006). The immersed interface method: Numerical solutions of PDEs involving interfaces and irregular domains. https://doi.org/10.1137/1.9780898717464

Li, Z. (2005). Augmented Strategies for Interface and Irregular Domain Problems. In Z. Li, L. Vulkov, & J. Wasniewski (Eds.), Numerical Analysis and Its Applications (pp. 66–79). https://doi.org/10.1007/978-3-540-31852-1_7

Ito, K., Li, Z. L., & Kyei, Y. (2005). Higher-order, Cartesian grid based finite difference schemes for elliptic equations on irregular domains. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 27(1), 346–367. https://doi.org/10.1137/03060120X

Li, Z., & Yang, X. (2005). Immersed finite element for elasticity system with discontinuities. AMS Contemporary Mathematics, 383, 285–298.

Li, Z., Vulkov, L., & Waśniewski, J. (Eds.). (2005). Numerical Analysis and Its Applications. https://doi.org/10.1007/b106395

Li, Z., Lin, T., Lin, Y., & Rogers, R. C. (2004). An immersed finite element space and its approximation capability. Numerical Methods for Partial Differential Equations, 20(3), 338–367. https://doi.org/10.1002/num.10092

Zolotarevskii, V. A., Li, Z. L., & Caraus, I. (2004). Approximate solution of singular integro-differential equations by reduction over Faber-Laurent polynomials. DIFFERENTIAL EQUATIONS, 40(12), 1764–1769. https://doi.org/10.1007/s10625-005-0108-3

Li, Z., & Wang, C. (2003). A Fast Finite Differenc Method For Solving Navier-Stokes Equations on Irregular Domains. Communications in Mathematical Sciences, 1(1), 180–196. https://doi.org/10.4310/cms.2003.v1.n1.a11

Li, Z. (2003). An overview of the immersed interface method and its applications. Taiwanese Journal of Mathematics, 7(1), 1–49. https://doi.org/10.11650/twjm/1500407515

Li, Z., Lin, X., Torres, M., & Zhao, H. (2003). Generalized Snell's Law for Weighted Minimal Surface in Heterogeneous Media. Methods and Applications of Analysis, 10(2), 199–214. https://doi.org/10.4310/maa.2003.v10.n2.a3

Li, Z. L., Lin, T., & Wu, X. H. (2003). New Cartesian grid methods for interface problems using the finite element formulation. NUMERISCHE MATHEMATIK, 96(1), 61–98. https://doi.org/10.1007/s00211-003-0473-x

Li, Z. L., Wang, W. C., Chern, I. L., & Lai, M. C. (2003). New formulations for interface problems in polar coordinates. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 25(1), 224–245. https://doi.org/10.1137/S106482750139618X

Ito, K., & Li, Z. L. (2003). Solving a nonlinear problem in magneto-rheological fluids using the immersed interface method. JOURNAL OF SCIENTIFIC COMPUTING, 19(1-3), 253–266. https://doi.org/10.1023/A:1025356025745

Yang, X. Z., Li, B., & Li, Z. L. (2003). The  immersed interface method for elasticity problems with interfaces. Dynamics of Continuous, Discrete & Impulsive Systems. Series A, Mathematical Analysis, 10(5), 783–808.

Deng, S. Z., Ito, K., & Li, Z. L. (2003). Three-dimensional elliptic solvers for interface problems and applications. JOURNAL OF COMPUTATIONAL PHYSICS, 184(1), 215–243. https://doi.org/10.1016/S0021-9991(02)00028-1

Lubkin, S. R., & Li, Z. (2002). Force and deformation on branching rudiments: cleaving between hypotheses. BIOMECHANICS AND MODELING IN MECHANOBIOLOGY, 1(1), 5–16. https://doi.org/10.1007/s10237-002-0001-4

Gremaud, P., Li, Z., Smith, R., & Tran, H. (Eds.). (2002). Industrial Mathematics Modeling Workshop for Graduate Students Series [CRSC Technical Reports].

Hunter, J. K., Li, Z. L., & Zhao, H. K. (2002). Reactive autophobic spreading of drops. JOURNAL OF COMPUTATIONAL PHYSICS, 183(2), 335–366. https://doi.org/10.1006/jcph.2002.7168

Adams, L., & Li, Z. L. (2002). The immersed interface/multigrid methods for interface problems. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 24(2), 463–479. https://doi.org/10.1137/S1064827501389849

Li, Z., & Cai, W. (2001). A Level Set-Boundary Element Method for Simulation of Dynamic Powder Consolidation of Metals. In J. W. L. Vulkov & P. Yalamov (Eds.), Lecture Notes in Computer Science (Vol. 1988, pp. 527–534). https://doi.org/10.1007/3-540-45262-1_62

Lai, M. C., & Li, Z. L. (2001). A remark on jump conditions for the three-dimensional Navier-Stokes equations involving an immersed moving membrane. APPLIED MATHEMATICS LETTERS, 14(2), 149–154. https://doi.org/10.1016/S0893-9659(00)00127-0

Li, Z. (2001). Book Review: Generalized Difference Methods for Differential Equations [Review of Generalized Difference Methods for Differential Equations, by Z. Chen, R. Li, & W. Wu]. SIAM Review, 43(1), 203–205,

Gremaud, P., Li, Z., Smith, R., & Tran, H. (Eds.). (2001). Industrial Mathematics Modeling Workshop for Graduate Students Series [CRSC Technical Reports].

Ito, K., Kunisch, K., & Li, Z. L. (2001). Level-set function approach to an inverse interface problem. INVERSE PROBLEMS, 17(5), 1225–1242. https://doi.org/10.1088/0266-5611/17/5/301

Li, Z. L., & Ito, K. (2001). Maximum principle preserving schemes for interface problems with discontinuous coefficients. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 23(1), 339–361. https://doi.org/10.1137/S1064827500370160

Li, Z. (2001). Numerical Method for Simulation of Bubbles Flowing Through Another Fluid. In M. Mu, Z. Shi, W. Xue, & J. Zou (Eds.), Advances in Scientific Computing (pp. 74–81). Beijing: Science Pr.

Li, Z. L., & Lubkin, SR. (2001). Numerical analysis of interfacial two-dimensional Stokes flow with discontinuous viscosity and variable surface tension. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 37(5), 525–540. https://doi.org/10.1002/fld.185

Li, Z. L., & Lai, M. C. (2001). The immersed interface method for the Navier-Stokes equations with singular forces. JOURNAL OF COMPUTATIONAL PHYSICS, 171(2), 822–842. https://doi.org/10.1006/jcph.2001.6813

Gremaud, P., Li, Z., Smith, R., & Tran, H. (Eds.). (2000). Industrial Mathematics. Philadelphia: SIAM.

Gremaud, P., Li, Z., Smith, R., & Tran, H. (Eds.). (2000). Industrial Mathematics Modeling Workshop for Graduate Students Series [CRSC Technical Reports].

Li, Z., & Shen, Y.-Q. (1999). A numerical method for solving heat equations involving interfaces. Electronic Journal of Differential Equations, 3, 100–108.

Li, Z. L., Zhao, H. K., & Gao, H. J. (1999). A numerical study of electro-migration voiding by evolving level set functions on a fixed Cartesian grid. JOURNAL OF COMPUTATIONAL PHYSICS, 152(1), 281–304. https://doi.org/10.1006/jcph.1999.6249

Huang, H. X., & Li, Z. L. (1999). Convergence analysis of the immersed interface method. IMA JOURNAL OF NUMERICAL ANALYSIS, 19(4), 583–608. https://doi.org/10.1093/imanum/19.4.583

Wiegmann, A., Li, Z., & LeVeque, R. J. (1999). Crack jump conditions for elliptic problems. APPLIED MATHEMATICS LETTERS, 12(6), 81–88. https://doi.org/10.1016/S0893-9659(99)00083-X

Li, Z. L., & Soni, B. (1999). Fast and accurate numerical approaches for Stefan problems and crystal growth. NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS, 35(4), 461–484. https://doi.org/10.1080/104077999275848

Gremaud, P., Li, Z., Smith, R., & Tran, H. (Eds.). (1999). Industrial Mathematics Modeling Workshop for Graduate Students series [CRSC Technical Reports].

Gao, H., Li, Z., & Zhao, H. (1999). Numerical Study of Two Dimensional Electro-migration. Journal of Computational Physics, 152, 281–304.

Ewing, R. E., Li, Z. L., Lin, T., & Lin, Y. P. (1999). The immersed finite volume element methods for the elliptic interface problems. MATHEMATICS AND COMPUTERS IN SIMULATION, 50(1-4), 63–76. https://doi.org/10.1016/S0378-4754(99)00061-0

Li, Z., & Putcha, M. (1999). Types of reductive monoids. Journal of Algebra, 221(1), 102–116. https://doi.org/10.1006/jabr.1999.7946

Li, Z. L. (1998). A fast iterative algorithm for elliptic interface problems. SIAM JOURNAL ON NUMERICAL ANALYSIS, 35(1), 230–254. https://doi.org/10.1137/S0036142995291329

Li, Z. L. (1998). The immersed interface method using a finite element formulation. APPLIED NUMERICAL MATHEMATICS, 27(3), 253–267. https://doi.org/10.1016/S0168-9274(98)00015-4

Li, Z., Wang, D., & Zou, J. (1998). Theoretical and numerical analysis on a thermo-elastic system with discontinuities. Journal of Computational and Applied Mathematics, 92(1), 37–58. https://doi.org/10.1016/s0377-0427(98)00044-2

Hou, T. Y., Li, Z., Osher, S., & Zhao, H. (1997). A Hybrid Method for Moving Interface Problems with Application to the Hele–Shaw Flow. Journal of Computational Physics, 134(2), 236–252. https://doi.org/10.1006/jcph.1997.5689

Li, Z., & Zheng, K. (1997). An Inverse Problem in a Parabolic Equation. Electronic Journal of Differential Equations, 1, 193–199.

Heine, J. T., Li, Z., & McTigue, D. F. (1997). Front fixing vs. front tracking for diffusive transport with moving boundaries. International Journal for Numerical & Analytical Methods in Geomechanics, 21, 653–662.

LeVeque, R. J., & Li, Z. (1997). Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension. SIAM Journal on Scientific Computing, 18(3), 709–735. https://doi.org/10.1137/s1064827595282532

Li, Z. (1997). Immersed interface methods for moving interface problems. Numerical Algorithms, 14, 269–293. https://doi.org/10.1023/A:1019173215885

Li, Z. (1996). A note on immersed interface method for three-dimensional elliptic equations. Computers & Mathematics with Applications, 31(3), 9–17. https://doi.org/10.1016/0898-1221(95)00202-2

LeVeque, R. J., & Li, Z. (1995). Simulation of bubbles in creeping flow using the immersed interface method. Proceedings of the sixth international symposium on computational fluid dynamics, 688–693.

LeVeque, R. J., & Li, Z. (1994). The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources. SIAM Journal on Numerical Analysis, 31(4), 1019–1044. https://doi.org/10.1137/0731054

Li, Z. (1994). The Immersed Interface Method — A Numerical Approach for Partial Differential Equations with Interfaces (PhD thesis). University of Washington.

Li, Z., & Mayo, A. (1993). ADI methods for heat equations with discontinuities along an arbitrary interface. In W. Gautschi (Ed.), Proceedings of Symposia in Applied Mathematics (Vol. 48, pp. 311–315). Providence, Rhode Island: AMS.

Huang, K., & Li, Z. (1990). Perturbation theorems of eigenvectors. Numerical Mathematics, a Journal of Chinese Universities, 12(3), 284–289.

Huang, K., & Li, Z. (1989). Roundoff error analysis for polynomial interpolation. Research and Review in Mathematics, (2).

Li, Z. (1989). The uniform treatment for linear system — Algorithm and numerical stability. Journal on Numerical Methods & Computer Applications, 10(2).

Li, Z. (1988). Optimal conjugate gradient method for solving arbitrary linear equations. Journal of Nanjing Normal University (Natural Science Edition), (3), 28–34.

Li, Z. (1987). A generalized conjugate gradient method for solving real skew-symmetric systems. Journal on Numerical Methods & Computer Applications, 8(4), 31–37.

Huang, K., & Li, Z. (1987). An equivalent theorem on the numerical stability for an algorithm. Numerical Mathematics, a Journal of Chinese Universities, 9(1), 59–65.

Huang, K., & Li, Z. (1985). On the relation between the behavior and the distribution of the zeros of a polynomial. Journal of Nanjing University, Mathematics Biquarterly, 2(1), 53–59.

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