Works (199)
2025 article
A fourth order mixed compact finite difference scheme for biharmonic equations
Pan, K., Li, J., Li, Z., & Hu, H. (2025, July 27). Journal of Computational Physics, Vol. 539.
2025 article
A unified approach to high-order compact finite difference schemes for 3D Poisson equations
Fu, K., Hu, H., Li, Z., & Pan, K. (2025, September 10). Journal of Computational and Applied Mathematics, Vol. 475.
2025 article
An Immersed Finite Element Method for Anisotropic Elliptic Interface Problems with Nonhomogeneous Jump Conditions
Ji, H., & Li, Z. (2025, December 12). Journal of Scientific Computing.
2025 article
Convergence study of IB methods for Stokes equations with prescribed velocity boundary conditions
Li, Z., Pan, K., & Ruiz-Álvarez, J. (2025, February 7). IMA Journal of Numerical Analysis, Vol. 2.
2024 article
A Direct Method for Solving Three-Dimensional Elliptic Interface Problems
Gamage, K. G. K., Peng, Y. P. Y., & Li, Z. L. Z. (2024, May 20). International Journal of Numerical Analysis and Modeling, Vol. 21, pp. 353–374.
2024 article
A generalized level-set immersed interface method with application
Xu, J.-J., & Li, Z. (2024, August 23). Computers & Fluids, Vol. 283.
2024 article
Coupled transformation methods and analysis for BVPs on infinite domains
Li, Z., & Pan, K. (2024, January 17). Journal of Computational and Applied Mathematics, Vol. 444.
2024 article
Fully accurate approximation of piecewise smooth functions using corrected B-spline quasi-interpolants
Li, Z., Pan, K., Ruiz, J., & Yáñez, D. F. (2024, April 8). Computational and Applied Mathematics, Vol. 43.
open access via link.springer.com (publisher PDF)
2024 article
High order compact augmented methods for Stokes equations with different boundary conditions
Pan, K., Li, J., & Li, Z. (2024, May 8). Computer Physics Communications, Vol. 301.
2024 article
New third-order convex splitting methods and analysis for the phase field crystal equation
Ye, Z., Zheng, Z., & Li, Z. (2024, February 28). Numerical Algorithms, Vol. 2.
2024 article
The Immersed Interface Method for Navier-Stokes Equations with Interfaces in Cylindrical Coordinates
Ruiz-Álvarez, J., Dong, B., & Li, Z. (2024, December 28). Communications on Applied Mathematics and Computation, Vol. 12.
2023 article
A Cell-Centered Multigrid Solver for the Finite Volume Discretization of Anisotropic Elliptic Interface Problems on Irregular Domains
Pan, K., Wu, X., Hu, H., & Li, Z. (2023, December 13). Journal of Computational Mathematics, Vol. 12.
2023 article
A Stable FE-FD Method for Anisotropic Parabolic PDEs with Moving Interfaces
Dong, B., Li, Z., & Ruiz-Álvarez, J. (2023, July 10). Communications on Applied Mathematics and Computation, Vol. 7.
2023 article
A pressure Poisson equation-based second-order method for solving two-dimensional moving contact line problems with topological changes
Chai, S., Li, Z., Zhang, Z., Zhang, Z., Zhang, Z., & Zhang, Z. (2023, November 22). Computers & Fluids, Vol. 269.
2023 article
Accurate derivatives approximations and applications to some elliptic PDEs using HOC methods
Li, J., Li, Z., & Pan, K. (2023, August 8). Applied Mathematics and Computation, Vol. 459.
2023 article
Adapting Cubic Hermite Splines to the Presence of Singularities Through Correction Terms
Amat, S., Li, Z., Ruiz-Álvarez, J., Solano, C., & Trillo, J. C. (2023, May 3). Journal of Scientific Computing, Vol. 95.
2023 article
Analysis of nonconforming IFE methods and a new scheme for elliptic interface problems
Ji, H., Wang, F., Chen, J., & Li, Z. (2023, May 18). ESAIM. Mathematical Modelling and Numerical Analysis, Vol. 57, pp. 2041–2076.
2023 article
High Order Compact Schemes for Flux Type BCs
Li, Z., & Pan, K. (2023, April 12). SIAM Journal on Scientific Computing, Vol. 45, pp. A646–A674.
2023 article
Higher Order Finite Element Methods for Some One-dimensional Boundary Value Problems
Dong, B., Li, Z., & Ruiz-Álvarez, J. (2023, January 6). Research Reports on Computer Science, Vol. 2, pp. 15–27.
2023 article
Higher Order Finite Element Methods for Some One-dimensional Boundary Value Problems
Dong, B., Li, Z., & Ruiz-Álvarez, J. (2023, January 16). Research Reports on Computer Science.
2023 article
New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations
Hu, H. H. H., Pan, K. P. K., Li, Z. L. Z., Fu, K. F. K., Li, J. L. J., Hu, H. H. H., & Li, Z. L. Z. (2023, April 9). Numerical Mathematics Theory Methods and Applications, Vol. 16, pp. 393–409.
2023 article
Numerical integration rules with improved accuracy close to discontinuities
Amat, S., Li, Z., Ruiz-Álvarez, J., Solano, C., & Trillo, J. C. (2023, March 29). Mathematics and Computers in Simulation, Vol. 210, pp. 593–614.
2023 article
Stable high order FD methods for interface and internal layer problems based on non-matching grids
Li, Z., Pan, K., & Ruiz-Álvarez, J. (2023, November 6). Numerical Algorithms, Vol. 11.
2022 article
A Variant Modified Skew-Normal Splitting Iterative Method for Non-Hermitian Positive Definite Linear Systems
Li, Z.-L. L. Z.-L., Li, R. L. R., Yin, J.-F. Y. J.-F., & Li, Z.-L. L. Z.-L. (2022, March 22). Numerical Mathematics Theory Methods and Applications, Vol. 2.
2022 article
A new parameter free partially penalized immersed finite element and the optimal convergence analysis
Ji, H., Wang, F., Chen, J., & Li, Z. (2022, March 24). Numerische Mathematik, Vol. 4.
2022 article
An $L^{\infty}$ Second Order Cartesian Method for 3D Anisotropic Interface Problems
Dong, B., Feng, X., & Li, Z. (2022, June 1). Journal of Computational Mathematics, pp. ["882–912"].
2022 article
An efficient extrapolation multigrid method based on a HOC scheme on nonuniform rectilinear grids for solving 3D anisotropic convection–diffusion problems
Hu, S., Pan, K., Wu, X., Ge, Y., & Li, Z. (2022, November 5). Computer Methods in Applied Mechanics and Engineering, Vol. 403.
2022 article
An immersed CR-P0 element for Stokes interface problems and the optimal convergence analysis
Ji, H., Wang, F., Chen, J., & Li, Z. (2022, July 13). Computer Methods in Applied Mechanics and Engineering, Vol. 9.
2022 article
Numerical analysis of a free boundary problem with non-local obstacles
Li, Z., & Mikayelyan, H. (2022, August 30). Applied Mathematics Letters, Vol. 1.
2021 article
A High Order Compact FD Framework for Elliptic BVPs Involving Singular Sources, Interfaces, and Irregular Domains
Pan, K., He, D., & Li, Z. (2021, July 28). Journal of Scientific Computing, Vol. 88.
2021 article
A generalized modulus-based Newton method for solving a class of non-linear complementarity problems with P-matrices
Li, R., Li, Z.-L., & Yin, J.-F. (2021, June 3). Numerical Algorithms, Vol. 6.
2021 article
A new FV scheme and fast cell-centered multigrid solver for 3D anisotropic diffusion equations with discontinuous coefficients
Pan, K., Wu, X., Hu, H., Yu, Y., & Li, Z. (2021, October 22). Journal of Computational Physics, Vol. 449, p. 110794.
2021 article
A new patch up technique for elliptic partial differential equation with irregularities
Singh, S., Singh, S., & Li, Z. (2021, December 29). Journal of Computational and Applied Mathematics, Vol. 6.
2021 article
An ADI-Yee's scheme for Maxwell's equations with discontinuous coefficients
Deng, S., Li, Z., & Pan, K. (2021, April 16). Journal of Computational Physics, Vol. 438, p. 110356.
2021 article
An Acceleration Technique for the Augmented IIM for 3D Elliptic Interface Problems
Zhang, C. Z. C., Li, Z. L. Z., & Yue, X. Y. X. (2021, June 1). Numerical Mathematics Theory Methods and Applications, Vol. 8.
2021 article
Fourth order compact FD methods for convection diffusion equations with variable coefficients
Tong, F., Feng, X., & Li, Z. (2021, May 16). Applied Mathematics Letters, Vol. 121, p. 107413.
2021 article
Optimal convergence of three iterative methods based on nonconforming finite element discretization for 2D/3D MHD equations
Xu, J., Su, H., & Li, Z. (2021, November 13). Numerical Algorithms, Vol. 11.
2021 journal article
Partially penalized IFE methods and convergence analysis for elasticity interface problems
Journal of Computational and Applied Mathematics.
2021 article
Quadratic hyper-surface kernel-free least squares support vector regression
Ye, J., Yang, Z., & Li, Z. (2021, March 4). Intelligent Data Analysis, Vol. 25, pp. 265–281.
2021 article
The local tangential lifting method for moving interface problems on surfaces with applications
Xiao, X., Feng, X., & Li, Z. (2021, January 19). Journal of Computational Physics, Vol. 431, p. 110146.
2020 article
An FE-FD Method for Anisotropic Elliptic Interface Problems
Dong, B., Feng, X., & Li, Z. (2020, January 1). SIAM Journal on Scientific Computing, Vol. 42, pp. B1041–B1066.
2020 book
Introduction to Partial Differential Equations
In WORLD SCIENTIFIC eBooks.
2020 article
Non-parallel hyperplanes ordinal regression machine
Jiang, H., Yang, Z., & Li, Z. (2020, November 9). Knowledge-Based Systems, Vol. 11, p. 106593.
2020 article
Partially penalized IFE methods and convergence analysis for elasticity interface problems
Huang, P., & Li, Z. (2020, June 20). Journal of Computational and Applied Mathematics, Vol. 382.
2019 article
A gradient recovery–based adaptive finite element method for convection‐diffusion‐reaction equations on surfaces
Xiao, X., Feng, X., & Li, Z. (2019, July 4). International Journal for Numerical Methods in Engineering.
2019 article
An Augmented IB Method & Analysis for Elliptic BVP on Irregular Domains
Li, Z., Dong, B., Tong, F., & Wang, W. (2019, January 1). Computer Modeling in Engineering & Sciences, Vol. 119, pp. 63–72.
2019 article
Analysis of Network Structure of Urban Bike-Sharing System: A Case Study Based on Real-Time Data of a Public Bicycle System
Yao, Y., Zhang, Y., Tian, L., Zhou, N., Li, Z., & Wang, M. (2019, September 30). Sustainability, Vol. 11.
2019 article
How to obtain an accurate gradient for interface problems?
Tong, F., Wang, W., Feng, X., Zhao, J., & Li, Z. (2019, November 1). Journal of Computational Physics, Vol. 405, p. 109070.
2019 article
Numerical Validations of the Tangent Linear Model for the LorenzEquations
Zhao, T., Zhang, J., Li, Z., & Zhang, Z. (2019, January 1). Computer Modeling in Engineering & Sciences, Vol. 120, pp. 83–104.
2019 article
Spatiotemporal characteristics of green travel: A classification study on a public bicycle system
Yao, Y., Jiang, X., & Li, Z. (2019, August 2). Journal of Cleaner Production, Vol. 238.
2018 article
A direct IIM approach for two-phase Stokes equations with discontinuous viscosity on staggered grids
Chen, X., Li, Z., & Álvarez, J. R. (2018, March 10). Computers & Fluids, Vol. 172, pp. 549–563.
2018 article
A direct method for accurate solution and gradient computations for elliptic interface problems
Chen, X., Feng, X., & Li, Z. (2018, March 7). Numerical Algorithms, Vol. 80, pp. 709–740.
2018 article
A high-order source removal finite element method for a class of elliptic interface problems
Ji, H., Chen, J., & Li, Z. (2018, April 5). Applied Numerical Mathematics, Vol. 130, pp. 112–130.
2018 article
A least squares augmented immersed interface method for solving Navier–Stokes and Darcy coupling equations
Li, Z., Lai, M.-C., Peng, X., & Zhang, Z. (2018, March 18). Computers & Fluids, Vol. 167, pp. 384–399.
2018 article
Error analysis of the immersed interface method for Stokes equations with an interface
Hu, R., & Li, Z. (2018, April 12). Applied Mathematics Letters, Vol. 83, pp. 207–211.
2018 book
Numerical solution of differential equations: Introduction to finite difference and finite element methods
New York: Cambridge University Press.
2018 article
On MultiScale ADI Methods for Parabolic PDEs with a Discontinuous Coefficient
Li, Z., Chen, X., & Zhang, Z. (2018, January 1). Multiscale Modeling and Simulation, Vol. 16, pp. 1623–1647.
2017 article
A Uniformly Stable Nonconforming FEM Based on Weighted Interior Penalties for Darcy-Stokes-Brinkman Equations
Huang, P., & Li, Z. (2017, February 1). Numerical Mathematics Theory Methods and Applications, Vol. 10, pp. 22–43.
2017 article
Accurate Solution and Gradient Computation for Elliptic Interface Problems with Variable Coefficients
Li, Z., Ji, H., & Chen, X. (2017, January 1). SIAM Journal on Numerical Analysis, Vol. 55, pp. 570–597.
2017 article
Accurate gradient computations at interfaces using finite element methods
Qin, F., Wang, Z., Ma, Z., & Li, Z. (2017, September 1). International Journal of Applied Mathematics and Computer Science, Vol. 27, pp. 527–537.
2017 article
An Augmented Method for 4th Order PDEs with Discontinuous Coefficients
Li, Z., & Qin, F. (2017, June 23). Journal of Scientific Computing, Vol. 73, pp. 968–979.
2017 journal article
An augmented IIM & preconditioning technique for jump embedded boundary conditions
An augmented IIM & preconditioning technique for jump embedded boundary conditions. International Journal of Numerical Analysis and Modeling, 14(4-5), 712–729.
2017 article
New Conservative Finite Volume Element Schemes for the Modified Regularized Long Wave Equation
Yan, J., Lai, M.-C., Li, Z., & Zhang, Z. (2017, January 9). Advances in Applied Mathematics and Mechanics, Vol. 9, pp. 250–271.
2017 article
Numerical Solution of Differential Equations
Li, Z., Qiao, Z., & Tang, T. (2017, November 17). Cambridge University Press EBooks.
2017 journal article
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.
2016 article
A Cartesian grid nonconforming immersed finite element method for planar elasticity interface problems
Qin, F., Chen, J., Li, Z., & Cai, M. (2016, December 18). Computers & Mathematics with Applications, Vol. 73, pp. 404–418.
2016 journal article
An augmented iim for helmholtz/poisson equations on irregular domains in complex space
International Journal of Numerical Analysis and Modeling, 13(1), 166–178.
2016 article
Fine numerical analysis of the crack-tip position for a Mumford–Shah minimizer
Li, Z., & Mikayelyan, H. (2016, June 6). Interfaces and Free Boundaries Mathematical Analysis Computation and Applications, Vol. 18, pp. 75–90.
2016 journal article
Fourth-order compact schemes for Helmholtz equations with piecewise wave numbers in the polar coordinates
Journal of Computational Mathematics, 34(5), 499–510.
2016 article
Prioritization of pesticides based on daily dietary exposure potential as determined from the SHEDS model
Melnyk, L. J., Wang, Z., Li, Z., & Xue, J. (2016, August 5). Food and Chemical Toxicology, Vol. 96, pp. 167–173.
2016 journal article
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.
2015 article
A Sparse Grid Stochastic Collocation Method for Elliptic Interface Problems with Random Input
Zhang, Q., Li, Z., & Zhang, Z. (2015, August 3). Journal of Scientific Computing, Vol. 67, pp. 262–280.
2015 article
A new augmented immersed finite element method without using SVD interpolations
Ji, H., Chen, J., & Li, Z. (2015, May 8). Numerical Algorithms, Vol. 71, pp. 395–416.
2015 article
A semi-implicit augmented IIM for Navier–Stokes equations with open, traction, or free boundary conditions
Li, Z., Xiao, L., Cai, Q., Zhao, H., & Luo, R. (2015, May 27). Journal of Computational Physics.
2015 article
An augmented Cartesian grid method for Stokes–Darcy fluid–structure interactions
Li, Z. (2015, September 11). International Journal for Numerical Methods in Engineering, Vol. 106, pp. 556–575.
2015 article
An immersed finite volume element method for 2D PDEs with discontinuous coefficients and non-homogeneous jump conditions
Zhu, L., Zhang, Z., & Li, Z. (2015, May 15). Computers & Mathematics with Applications, Vol. 70, pp. 89–103.
2015 article
Augmented immersed finite element methods for some elliptic partial differential equations
Ji, H., Chen, J., & Li, Z. (2015, January 13). International Journal of Computer Mathematics, Vol. 93, pp. 540–558.
2015 article
Effective matrix-free preconditioning for the augmented immersed interface method
Xia, J., Li, Z., & Ye, X. (2015, October 15). Journal of Computational Physics, Vol. 303, pp. 295–312.
2015 article
Immersed finite elements for optimal control problems of elliptic PDEs with interfaces
Zhang, Q., Ito, K., Li, Z., & Zhang, Z. (2015, June 18). Journal of Computational Physics, Vol. 298, pp. 305–319.
2015 article
The immersed interface method for axis-symmetric problems and application to the Hele–Shaw flow
Álvarez, J. R., & Li, Z. (2015, May 14). Applied Mathematics and Computation, Vol. 264, pp. 179–197.
2014 article
A Symmetric and Consistent Immersed Finite Element Method for Interface Problems
Ji, H., Chen, J., & Li, Z. (2014, March 17). Journal of Scientific Computing, Vol. 61, pp. 533–557.
2014 journal article
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.
2014 article
A parallel Robin–Robin domain decomposition method for H(div)-elliptic problems
Zeng, Y., Chen, J., & Li, Z. (2014, February 14). International Journal of Computer Mathematics, Vol. 92, pp. 394–410.
2014 journal article
On convergence of the immersed boundary method for elliptic interface problems
Mathematics of Computation, 84(293), 1169–1188.
2014 journal article
Special issue on fluid structure interactions preface
Numerical Mathematics: Theory, Methods and Applications, 7(4), I-.
2013 article
A Coupled Immersed Interface and Level Set Method for Three-Dimensional Interfacial Flows with Insoluble Surfactant
Xu, J.-J., Huang, Y., Lai, M.-C., & Li, Z. (2013, September 10). Communications in Computational Physics, Vol. 15, pp. 451–469.
2013 article
A Fourier finite volume element method for solving two-dimensional quasi-geostrophic equations on a sphere
Wang, Q., Zhang, Z., & Li, Z. (2013, April 29). Applied Numerical Mathematics, Vol. 71, pp. 1–13.
2013 article
Adaptive mesh refinement techniques for the immersed interface method applied to flow problems
Li, Z., & Song, P. (2013, April 17). Computers & Structures, Vol. 122, pp. 249–258.
2013 article
Exploring accurate Poisson–Boltzmann methods for biomolecular simulations
Wang, C., Wang, J., Cai, Q., Li, Z., Zhao, H.-K., & Luo, R. (2013, September 27). Computational and Theoretical Chemistry.
2013 article
Some new analysis results for a class of interface problems
Li, Z., Wang, L., Aspinwall, E., Cooper, R., Kuberry, P., Sanders, A., & Zeng, K. (2013, June 20). Mathematical Methods in the Applied Sciences, Vol. 38, pp. 4530–4539.
2012 article
A Numerical Method for Solving Elasticity Equations with Interfaces
Hou, S., Li, Z., Wang, L., & Wang, W. (2012, May 22). Communications in Computational Physics, Vol. 12, pp. 595–612.
2012 article
An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods
Li, Z., & Song, P. (2012, May 22). Communications in Computational Physics, Vol. 12, pp. 515–527.
2012 article
An augmented immersed interface method for moving structures with mass
Hao, J., Li, Z., & Lubkin, S. R. (2012, January 1). Discrete and Continuous Dynamical Systems - B, Vol. 17, pp. 1175–1184.
Contributors: J. Ho n, * & S. Lubkin*
2012 article
Exploring a charge-central strategy in the solution of Poisson's equation for biomolecular applications
Liu, X., Wang, C., Wang, J., Li, Z., Zhao, H., & Luo, R. (2012, October 24). Physical Chemistry Chemical Physics, Vol. 15, pp. 129–141.
2012 article
Numerical Poisson–Boltzmann model for continuum membrane systems
Botello-Smith, W. M., Liu, X., Cai, Q., Li, Z., Zhao, H., & Luo, R. (2012, November 7). Chemical Physics Letters, Vol. 555, pp. 274–281.
2012 article
Numerical Solutions of the System of Singular Integro-Differential Equations in Classical Hölder Spaces
Caraus, I., & Li, Z. (2012, November 15). Advances in Applied Mathematics and Mechanics, Vol. 4, pp. 737–750.
2012 book
SPECIAL ISSUE ON FLUID DYNAMICS, ANALYSIS AND NUMERICS
2012 article
Simulation of Longitudinal Exposure Data with Variance‐Covariance Structures Based on Mixed Models
Song, P., Xue, J., & Li, Z. (2012, July 22). Risk Analysis, Vol. 33, pp. 469–479.
2012 article
Some new finite difference methods for Helmholtz equations on irregular domains or with interfaces
Wan, X., & Li, Z. (2012, January 1). Discrete and Continuous Dynamical Systems - B, Vol. 17, pp. 1155–1174.
2012 book
Special Issue on Fluid Motion Driven by Immersed Structures
In Global Sciences. https://www.researchgate.net/publication/296762774_Special_Issue_on_Fluid_Motion_Driven_by_Immersed_Structures_Preface
2012 journal article
Special issue on fluid motion driven by immersed structures preface
Communications in Computational Physics, 12(2), I-.
2012 article
The Sensitivity Analysis for the Flow Past Obstacles Problem with Respect to the Reynolds Number
Ito, K., Li, Z., & Qiao, Z. (2012, February 1). Advances in Applied Mathematics and Mechanics, Vol. 4, pp. 21–35.
2011 journal article
A finite element method for elasticity interface problems with locally modified triangulations
International Journal of Numerical Analysis and Modeling, 8(2), 189–200.
2011 journal article
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.
2011 journal article
High order compact finite difference schemes for the helmholtz equation with discontinuous coefficients
Journal of Computational Mathematics, 29(3), 324–340.
2011 article
Numerical Study of Surfactant-Laden Drop-Drop Interactions
Xu, J.-J., Li, Z., Lowengrub, J., & Zhao, H. (2011, April 29). Communications in Computational Physics, Vol. 10, pp. 453–473.
2010 article
An augmented method for free boundary problems with moving contact lines
Li, Z., Lai, M.-C., He, G., & Zhao, H. (2010, January 26). Computers & Fluids, Vol. 39, pp. 1033–1040.
2010 journal article
Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions
Numerical Mathematics: Theory, Methods and Applications, 3(1), 23–39.
2010 journal article
Simplified immersed interface methods for elliptic interface problems with straight interfaces
Numerical Methods for Partial Differential Equations, 28(1), 188–203.
2010 article
The IIM in polar coordinates and its application to electro capacitance tomography problems
Álvarez, J. R., Chen, J., & Li, Z. (2010, November 19). Numerical Algorithms, Vol. 57, pp. 405–423.
2009 article
A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations
Yang, X., Zhang, X., Li, Z., & He, G.-W. (2009, August 7). Journal of Computational Physics, Vol. 228, pp. 7821–7836.
2009 article
A well-conditioned augmented system for solving Navier–Stokes equations in irregular domains
Ito, K., Lai, M.-C., & Li, Z. (2009, January 2). Journal of Computational Physics, Vol. 228, pp. 2616–2628.
2009 conference paper
Analysis and computation for a fluid mixture model
Communications in Computational Physics, 5(2-4), 620–634.
2009 book
Interface Problems and Methods in Biological and Physical Flows
In B. C. Khoo, Z. Li, & P. Lin (Eds.), Lecture notes series, Institute For Mathematical Sciences.
Ed(s): B. Khoo *, n & P. Lin*
2009 book
Interface problems and methods in biological and physical flows
New Jersey: World Scientific.
2008 article
A finite element method for interface problems with locally modified triangulations
Xie, H., Ito, K., Li, Z., & Toivanen, J. (2008, January 1). Contemporary Mathematics - American Mathematical Society, Vol. 466, pp. 179–190.
2008 article
Achieving energy conservation in Poisson–Boltzmann molecular dynamics: Accuracy and precision with finite-difference algorithms
Wang, J., Cai, Q., Li, Z.-L., Zhao, H.-K., & Luo, R. (2008, December 25). Chemical Physics Letters, Vol. 468, pp. 112–118.
2008 article
An additive Schwarz preconditioner for the mortar-type rotated FEM for elliptic problems with discontinuous coefficients
Wang, F., Chen, J., Xu, W., & Li, Z. (2008, December 5). Applied Numerical Mathematics, Vol. 59, pp. 1657–1667.
2008 article
An explicit jump immersed interface method for two-phase Navier–Stokes equations with interfaces
Rutka, V., & Li, Z. (2008, January 9). Computer Methods in Applied Mechanics and Engineering, Vol. 197, pp. 2317–2328.
2008 article
An immersed interface method for solving incompressible viscous flows with piecewise constant viscosity across a moving elastic membrane
Tan, Z., Le, D. V., Li, Z., Lim, K. M., & Khoo, B. C. (2008, August 31). Journal of Computational Physics, Vol. 227, pp. 9955–9983.
2008 article
Immersed-Interface Finite-Element Methods for Elliptic Interface Problems with Nonhomogeneous Jump Conditions
Gong, Y., Li, B., & Li, Z. (2008, January 1). SIAM Journal on Numerical Analysis, Vol. 46, pp. 472–495.
2007 article
A fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow
Chen, G., Li, Z., & Lin, P. (2007, July 23). Advances in Computational Mathematics, Vol. 29, pp. 113–133.
2007 journal article
An augmented immersed interface-level set method for Stokes equations with discontinuous viscosity
Electronic Journal of Differential Equations, Conference, 15, 193–210.
2007 journal article
An immersed interface method for the Navier-Stokes equations on irregular domains
PAMM, 7(1), 1025401–1025402.
2007 article
Mechanics of mesenchymal contribution to clefting force in branching morphogenesis
Wan, X., Li, Z., & Lubkin, S. R. (2007, September 27). Biomechanics and Modeling in Mechanobiology, Vol. 7, pp. 417–426.
2007 book
Moving Interface Problems and Applications in Fluid Dynamics
In AMS Contemporary mathematics 466. https://books.google.com/books/about/Moving_Interface_Problems_and_Applicatio.html?id=fMYbCAAAQBAJ
2007 book
Special Issue for the International Conference on Scientific Computing
https://www.sciencedirect.com/journal/applied-numerical-mathematics/vol/57/issue/5
2006 article
A study of numerical methods for the level set approach
Gremaud, P. A., Kuster, C. M., & Li, Z. (2006, August 15). Applied Numerical Mathematics, Vol. 57, pp. 837–846.
2006 article
An augmented approach for Stokes equations with a discontinuous viscosity and singular forces
Li, Z., Ito, K., & Lai, M.-C. (2006, July 26). Computers & Fluids, Vol. 36, pp. 622–635.
2006 journal article
An augmented approach for the pressure boundary condition in a Stokes flow
Communications in Computational Physics, 1(5), 874–885.
2006 journal article
Efficient numerical methods for the 2D nonlinear Poisson–Boltzmann equation modeling charged spheres
Journal of Computational Mathematics, 24(3), 252–264.
2006 article
Preface of the special issue of APNUM International Conference on Scientific Computing in Nanjing, China
Li, Z., Song, Y., & Tang, T. (2006, July 30). Applied Numerical Mathematics, Vol. 57, pp. 473–474.
2006 article
The Immersed Interface Method
Li, Z., & Ito, K. (2006, January 1). Society for Industrial and Applied Mathematics EBooks.
2005 journal article
A Finite Difference Method and Analysis for 2D Nonlinear Poisson–Boltzmann Equations
Journal of Scientific Computing, 30(1), 61–81.
2005 article
A level-set method for interfacial flows with surfactant
Xu, J.-J., Li, Z., Lowengrub, J., & Zhao, H. (2005, September 10). Journal of Computational Physics, Vol. 212, pp. 590–616.
2005 chapter
Augmented Strategies for Interface and Irregular Domain Problems
In Z. Li, L. Vulkov, & J. Wasniewski (Eds.), Numerical Analysis and Its Applications (pp. 66–79).
2005 article
Fast solvers for 3D Poisson equations involving interfaces in a finite or the infinite domain
Lai, M.-C., Li, Z., & Lin, X. (2005, June 24). Journal of Computational and Applied Mathematics, Vol. 191, pp. 106–125.
2005 article
Higher-Order, Cartesian Grid Based Finite Difference Schemes for Elliptic Equations on Irregular Domains
Ito, K., Li, Z., & Kyei, Y. (2005, January 1). SIAM Journal on Scientific Computing, Vol. 27, pp. 346–367.
2005 journal article
Immersed finite element for elasticity system with discontinuities
AMS Contemporary Mathematics, 383, 285–298.
2005 article
Interface conditions for Stokes equations with a discontinuous viscosity and surface sources
Ito, K., & Li, Z. (2005, July 23). Applied Mathematics Letters, Vol. 19, pp. 229–234.
2005 book
Numerical Analysis and Its Applications
In Z. Li, L. Vulkov, & J. Waśniewski (Eds.), Lecture notes in computer science.
Ed(s): * , L. Vulkov * & J. Waśniewski*
2004 journal article
An immersed finite element space and its approximation capability
Numerical Methods for Partial Differential Equations, 20(3), 338–367.
2004 article
Approximate solution of singular integro-differential equations by reduction over Faber-Laurent polynomials
Zolotarevskii, V. A., Li, Z., & Caraus, I. (2004, December 1). Differential Equations, Vol. 40, pp. 1764–1769.
2003 journal article
A Fast Finite Differenc Method For Solving Navier-Stokes Equations on Irregular Domains
Communications in Mathematical Sciences, 1(1), 180–196.
2003 article
AN OVERVIEW OF THE IMMERSED INTERFACE METHOD AND ITS APPLICATIONS
Li, Z. (2003, March 1). Taiwanese Journal of Mathematics, Vol. 7, pp. 1–49.
2003 journal article
Generalized Snell's Law for Weighted Minimal Surface in Heterogeneous Media
Methods and Applications of Analysis, 10(2), 199–214.
2003 article
New Cartesian grid methods for interface problems using the finite element formulation
Li, Z., Lin, T., & Wu, X. (2003, November 1). Numerische Mathematik, Vol. 96, pp. 61–98.
2003 article
New Formulations for Interface Problems in Polar Coordinates
Li, Z., Wang, W.-C., Chern, I.-L., & Lai, M.-C. (2003, January 1). SIAM Journal on Scientific Computing, Vol. 25, pp. 224–245.
2003 article
Solving a Nonlinear Problem in Magneto-Rheological Fluids Using the Immersed Interface Method
Ito, K., & Li, Z. (2003, September 19). Journal of Scientific Computing, Vol. 19, pp. 253–266.
2003 journal article
The immersed interface method for elasticity problems with interfaces
Dynamics of Continuous, Discrete & Impulsive Systems. Series A, Mathematical Analysis, 10(5), 783–808.
2003 article
Three-dimensional elliptic solvers for interface problems and applications
Deng, S., Ito, K., & Li, Z. (2003, January 1). Journal of Computational Physics, Vol. 184, pp. 215–243.
2002 article
Force and deformation on branching rudiments: cleaving between hypotheses
Lubkin, S. R., & Li, Z. (2002, June 1). Biomechanics and Modeling in Mechanobiology, Vol. 1, pp. 5–16.
Contributors: S. Lubkin n & n
2002 article
Reactive Autophobic Spreading of Drops
Hunter, J. K., Li, Z., & Zhao, H. (2002, December 1). Journal of Computational Physics, Vol. 183, pp. 335–366.
2002 article
The Immersed Interface/Multigrid Methods for Interface Problems
Adams, L., & Li, Z. (2002, January 1). SIAM Journal on Scientific Computing, Vol. 24, pp. 463–479.
2001 chapter
A Level Set-Boundary Element Method for Simulation of Dynamic Powder Consolidation of Metals
In Lecture Notes in Computer Science (Vol. 1988, pp. 527–534).
Ed(s): J. L. Vulkov & P. Yalamov
2001 article
A remark on jump conditions for the three-dimensional Navier-Stokes equations involving an immersed moving membrane
Lai, M.-C., & Li, Z. (2001, February 1). Applied Mathematics Letters, Vol. 14, pp. 149–154.
2001 book review
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,
2001 article
Level-set function approach to an inverse interface problem
Ito, K., Kunisch, K., & Li, Z. (2001, August 30). Inverse Problems, Vol. 17, pp. 1225–1242.
2001 article
Maximum Principle Preserving Schemes for Interface Problems with Discontinuous Coefficients
Li, Z., & Ito, K. (2001, January 1). SIAM Journal on Scientific Computing, Vol. 23, pp. 339–361.
2001 chapter
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.
Ed(s): M. Mu, Z. Shi, W. Xue & J. Zou
Event: Workshop on Scientific Computing at Hong Kong
2001 article
Numerical analysis of interfacial two‐dimensional Stokes flow with discontinuous viscosity and variable surface tension
Li, Z., & Lubkin, S. R. (2001, October 8). International Journal for Numerical Methods in Fluids, Vol. 37, pp. 525–540.
Contributors: n & S. Lubkin n
2001 article
The Immersed Interface Method for the Navier–Stokes Equations with Singular Forces
Li, Z., & Lai, M.-C. (2001, August 1). Journal of Computational Physics, Vol. 171, pp. 822–842.
2000 book
1999 article
A Numerical Study of Electro-migration Voiding by Evolving Level Set Functions on a Fixed Cartesian Grid
Li, Z., Zhao, H., & Gao, H. (1999, June 1). Journal of Computational Physics, Vol. 152, pp. 281–304.
1999 journal article
A numerical method for solving heat equations involving interfaces
Electronic Journal of Differential Equations, 3, 100–108.
Event: Fourth Mississippi State Conference on Differential Equations and Computational Simulations, Conference 3
1999 article
Convergence analysis of the immersed interface method
Huang, H. X., & Li, Z. (1999, October 1). IMA Journal of Numerical Analysis, Vol. 19, pp. 583–608.
1999 article
Crack jump conditions for elliptic problems
Wiegmann, A., Li, Z., & LeVeque, R. J. (1999, August 1). Applied Mathematics Letters, Vol. 12, pp. 81–88.
1999 article
FAST AND ACCURATE NUMERICAL APPROACHES FOR STEFAN PROBLEMS AND CRYSTAL GROWTH
Li, Z., & Soni, B. (1999, June 1). Numerical Heat Transfer Part B Fundamentals, Vol. 35, pp. 461–484.
1999 journal article
Numerical Study of Two Dimensional Electro-migration
Journal of Computational Physics, 152, 281–304.
1999 article
The immersed finite volume element methods for the elliptic interface problems
Ewing, R. E., Li, Z., Lin, T., & Lin, Y. (1999, November 1). Mathematics and Computers in Simulation, Vol. 50, pp. 63–76.
1999 article
Types of Reductive Monoids
Li, Z., & Putcha, M. (1999, November 1). Journal of Algebra, Vol. 221, pp. 102–116.
1998 article
A Fast Iterative Algorithm for Elliptic Interface Problems
Li, Z. (1998, February 1). SIAM Journal on Numerical Analysis, Vol. 35, pp. 230–254.
1998 article
The immersed interface method using a finite element formulation
Li, Z. (1998, July 1). Applied Numerical Mathematics, Vol. 27, pp. 253–267.
1998 journal article
Theoretical and numerical analysis on a thermo-elastic system with discontinuities
Journal of Computational and Applied Mathematics, 92(1), 37–58.
1997 journal article
A Hybrid Method for Moving Interface Problems with Application to the Hele–Shaw Flow
Journal of Computational Physics, 134(2), 236–252.
1997 journal article
An Inverse Problem in a Parabolic Equation
Electronic Journal of Differential Equations, 1, 193–199.
Event: Conference
1997 journal article
Front fixing vs. front tracking for diffusive transport with moving boundaries
International Journal for Numerical & Analytical Methods in Geomechanics, 21, 653–662.
1997 journal article
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing, 18(3), 709–735.
1997 journal article
Immersed interface methods for moving interface problems
Numerical Algorithms, 14, 269–293.
1996 journal article
A note on immersed interface method for three-dimensional elliptic equations
Computers & Mathematics with Applications, 31(3), 9–17.
1995 conference paper
Simulation of bubbles in creeping flow using the immersed interface method
Proceedings of the sixth international symposium on computational fluid dynamics, 688–693.
Event: sixth international symposium on computational fluid dynamics at Lake Tahoe on September 4-8, 1995
1994 journal article
The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
SIAM Journal on Numerical Analysis, 31(4), 1019–1044.
1994 thesis
The Immersed Interface Method — A Numerical Approach for Partial Differential Equations with Interfaces
(PhD thesis). University of Washington.
1993 conference paper
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.
Ed(s): W. Gautschi
1990 journal article
Perturbation theorems of eigenvectors
Numerical Mathematics, a Journal of Chinese Universities, 12(3), 284–289.
1989 journal article
Roundoff error analysis for polynomial interpolation
Research and Review in Mathematics, (2).
1989 journal article
The uniform treatment for linear system — Algorithm and numerical stability
Journal on Numerical Methods & Computer Applications, 10(2).
1988 journal article
Optimal conjugate gradient method for solving arbitrary linear equations
Journal of Nanjing Normal University (Natural Science Edition), (3), 28–34.
1987 journal article
A generalized conjugate gradient method for solving real skew-symmetric systems
Journal on Numerical Methods & Computer Applications, 8(4), 31–37.
1987 journal article
An equivalent theorem on the numerical stability for an algorithm
Numerical Mathematics, a Journal of Chinese Universities, 9(1), 59–65.
1985 journal article
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.
book
Industrial Mathematics
In SIAM, USA.
book
Numerical Analysis and Its Applications
https://link.springer.com/book/10.1007%2Fb106395
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1994 - 1996