Immersed interface methods for moving interface problems. - Zhilin Li 002 (Numer. Algorithms, 1997)

Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension. - Randall J. LeVeque; Zhilin Li 002 (SIAM J. Sci. Comput., 1997)

A Level Set-Boundary Element Method for Simulation of Dynamic Powder Consolidation of Metals. - Zhilin Li 002; Wei Cai (NAA, 2000)

A remark on jump conditions for the three-dimensional Navier-Stokes equations involving an immersed moving membrane. - Ming-Chih Lai; Zhilin Li 002 (Appl. Math. Lett., 2001)

Maximum Principle Preserving Schemes for Interface Problems with Discontinuous Coefficients. - Zhilin Li 002; Kazufumi Ito (SIAM J. Sci. Comput., 2001)

The Immersed Interface/Multigrid Methods for Interface Problems. - Loyce Adams; Zhilin Li 002 (SIAM J. Sci. Comput., 2002)

Solving a Nonlinear Problem in Magneto-Rheological Fluids Using the Immersed Interface Method. - Kazufumi Ito; Zhilin Li 002 (J. Sci. Comput., 2003)

New Cartesian grid methods for interface problems using the finite element formulation. - Zhilin Li 002; Tao Lin 003; Xiaohui Wu (Numerische Mathematik, 2003)

New Formulations for Interface Problems in Polar Coordinates. - Zhilin Li 002; Wei-Cheng Wang; I-Liang Chern; Ming-Chih Lai (SIAM J. Sci. Comput., 2003)

Augmented Strategies for Interface and Irregular Domain Problems. - Zhilin Li 002 (NAA, 2004)

Higher-Order, Cartesian Grid Based Finite Difference Schemes for Elliptic Equations on Irregular Domains. - Kazufumi Ito; Zhilin Li 002; Yaw Kyei (SIAM J. Sci. Comput., 2005)

Interface conditions for Stokes equations with a discontinuous viscosity and surface sources. - Kazufumi Ito; Zhilin Li 002 (Appl. Math. Lett., 2006)

A level-set method for interfacial flows with surfactant. - Jian-Jun Xu; Zhilin Li 002; John S. Lowengrub; Hongkai Zhao (J. Comput. Phys., 2006)

A Finite Difference Method and Analysis for 2D Nonlinear Poisson-Boltzmann Equations. - Zhilin Li 002; C. V. Pao; Zhonghua Qiao (J. Sci. Comput., 2007)

Immersed-Interface Finite-Element Methods for Elliptic Interface Problems with Nonhomogeneous Jump Conditions. - Yan Gong; Bo Li 007; Zhilin Li 002 (SIAM J. Numer. Anal., 2007)

A fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow. - Guo Chen; Zhilin Li 002; Ping Lin (Adv. Comput. Math., 2008)

An immersed interface method for solving incompressible viscous flows with piecewise constant viscosity across a moving elastic membrane. - Zhijun Tan; Duc-Vinh Le; Zhilin Li 002; Kian Meng Lim; Boo Cheong Khoo (J. Comput. Phys., 2008)

A well-conditioned augmented system for solving Navier-Stokes equations in irregular domains. - Kazufumi Ito; Ming-Chih Lai; Zhilin Li 002 (J. Comput. Phys., 2009)

A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations. - Xiaolei Yang; Xing Zhang 004; Zhilin Li 002; Guo-Wei He (J. Comput. Phys., 2009)

The IIM in polar coordinates and its application to electro capacitance tomography problems. - Juan Ruiz-Álvarez 001; Jinru Chen; Zhilin Li 002 (Numer. Algorithms, 2011)

A Symmetric and Consistent Immersed Finite Element Method for Interface Problems. - Haifeng Ji; Jinru Chen; Zhilin Li 002 (J. Sci. Comput., 2014)

The immersed interface method for axis-symmetric problems and application to the Hele-Shaw flow. - Juan Ruiz-Álvarez 001; Zhilin Li 002 (Appl. Math. Comput., 2015)

An immersed finite volume element method for 2D PDEs with discontinuous coefficients and non-homogeneous jump conditions. - Ling Zhu; Zhiyue Zhang; Zhilin Li 002 (Comput. Math. Appl., 2015)

A parallel Robin-Robin domain decomposition method for H(div)-elliptic problems. - Yuping Zeng; Jinru Chen; Zhilin Li 002 (Int. J. Comput. Math., 2015)

A semi-implicit augmented IIM for Navier-Stokes equations with open, traction, or free boundary conditions. - Zhilin Li 002; Li Xiao; Qin Cai; Hongkai Zhao; Ray Luo 001 (J. Comput. Phys., 2015)

Effective matrix-free preconditioning for the augmented immersed interface method. - Jianlin Xia; Zhilin Li 002; Xin Ye 005 (J. Comput. Phys., 2015)

Immersed finite elements for optimal control problems of elliptic PDEs with interfaces. - Qian Zhang 039; Kazufumi Ito; Zhilin Li 002; Zhiyue Zhang (J. Comput. Phys., 2015)

On convergence of the immersed boundary method for elliptic interface problems. - Zhilin Li 002 (Math. Comput., 2015)

Augmented immersed finite element methods for some elliptic partial differential equations. - Haifeng Ji; Jinru Chen; Zhilin Li 002 (Int. J. Comput. Math., 2016)

A Sparse Grid Stochastic Collocation Method for Elliptic Interface Problems with Random Input. - Qian Zhang 039; Zhilin Li 002; Zhiyue Zhang (J. Sci. Comput., 2016)

A new augmented immersed finite element method without using SVD interpolations. - Haifeng Ji; Jinru Chen; Zhilin Li 002 (Numer. Algorithms, 2016)

Accurate gradient computations at interfaces using finite element methods. - Fangfang Qin; Zhaohui Wang; Zhijie Ma; Zhilin Li 002 (Int. J. Appl. Math. Comput. Sci., 2017)

A Cartesian grid nonconforming immersed finite element method for planar elasticity interface problems. - Fangfang Qin; Jinru Chen; Zhilin Li 002; Mingchao Cai (Comput. Math. Appl., 2017)

An Augmented Method for 4th Order PDEs with Discontinuous Coefficients. - Zhilin Li 002; Fangfang Qin (J. Sci. Comput., 2017)

Accurate Solution and Gradient Computation for Elliptic Interface Problems with Variable Coefficients. - Zhilin Li 002; Haifeng Ji; Xiaohong Chen 001 (SIAM J. Numer. Anal., 2017)

Error analysis of the immersed interface method for Stokes equations with an interface. - Rui Hu; Zhilin Li 002 (Appl. Math. Lett., 2018)

On an New Algorithm for Function Approximation with Full Accuracy in the Presence of Discontinuities Based on the Immersed Interface Method. - Sergio Amat; Zhilin Li 002; Juan Ruiz 001 (J. Sci. Comput., 2018)

On MultiScale ADI Methods for Parabolic PDEs with a Discontinuous Coefficient. - Zhilin Li 002; Xiao-hong Chen 001; Zhengru Zhang (Multiscale Model. Simul., 2018)

On jump relations of anisotropic elliptic interface problems. - Baiying Dong; Xiufang Feng; Zhilin Li 002 (CoRR, 2019)

A direct method for accurate solution and gradient computations for elliptic interface problems. - Xiaohong Chen 009; Xiufang Feng; Zhilin Li 002 (Numer. Algorithms, 2019)

How to obtain an accurate gradient for interface problems? - Fenghua Tong; Weilong Wang; Xinlong Feng; Jianping Zhao 001; Zhilin Li 002 (J. Comput. Phys., 2020)

An FE-FD Method for Anisotropic Elliptic Interface Problems. - Baiying Dong; Xiufang Feng; Zhilin Li 002 (SIAM J. Sci. Comput., 2020)

Fourth order compact FD methods for convection diffusion equations with variable coefficients. - Fenghua Tong; Xinlong Feng; Zhilin Li 002 (Appl. Math. Lett., 2021)

Analysis of nonconforming IFE methods and a new scheme for elliptic interface problems. - Haifeng Ji; Feng Wang 030; Jinru Chen; Zhilin Li 002 (CoRR, 2021)

An immersed CR-P0 element for Stokes interface problems and the optimal convergence analysis. - Haifeng Ji; Feng Wang 030; Jinru Chen; Zhilin Li 002 (CoRR, 2021)

A simple third order compact finite element method for 1D BVP. - Baiying Dong; Zhilin Li 002 (CoRR, 2021)

Convergence study of IB methods for Stokes equations with non-periodic boundary conditions. - Zhilin Li 002; Juan Ruiz-Álvarez 001 (CoRR, 2021)

Can 4th-order compact schemes exist for flux type BCs? - Zhilin Li 002; Kejia Pan (CoRR, 2021)

Quadratic hyper-surface kernel-free least squares support vector regression. - Junyou Ye; Zhixia Yang 001; Zhilin Li 002 (Intell. Data Anal., 2021)

Partially penalized IFE methods and convergence analysis for elasticity interface problems. - Peiqi Huang; Zhilin Li 002 (J. Comput. Appl. Math., 2021)

An ADI-Yee's scheme for Maxwell's equations with discontinuous coefficients. - Shaozhong Deng; Zhilin Li 002; Kejia Pan (J. Comput. Phys., 2021)

The local tangential lifting method for moving interface problems on surfaces with applications. - Xufeng Xiao; Xinlong Feng; Zhilin Li 002 (J. Comput. Phys., 2021)

A High Order Compact FD Framework for Elliptic BVPs Involving Singular Sources, Interfaces, and Irregular Domains. - Kejia Pan; Dongdong He; Zhilin Li 002 (J. Sci. Comput., 2021)

Non-parallel hyperplanes ordinal regression machine. - Haitao Jiang; Zhixia Yang; Zhilin Li 002 (Knowl. Based Syst., 2021)

High order two-grid finite difference methods for interface and internal layer problems. - Zhilin Li 002; Kejia Pan; Juan Ruiz-Álvarez 001 (CoRR, 2022)

Numerical integration rules with improved accuracy close to singularities. - Sergio Amat; Zhilin Li 002; Juan Ruiz-Álvarez 001; Concepcion Solano; Juan Carlos Trillo (CoRR, 2022)

A new patch up technique for elliptic partial differential equation with irregularities. - Swarn Singh; Suruchi Singh; Zhilin Li 002 (J. Comput. Appl. Math., 2022)

A new FV scheme and fast cell-centered multigrid solver for 3D anisotropic diffusion equations with discontinuous coefficients. - Kejia Pan; Xiaoxin Wu 003; Hongling Hu; Yunlong Yu; Zhilin Li 002 (J. Comput. Phys., 2022)

A generalized modulus-based Newton method for solving a class of non-linear complementarity problems with P-matrices. - Rui Li; Zhilin Li 002; Jun-Feng Yin (Numer. Algorithms, 2022)

Optimal convergence of three iterative methods based on nonconforming finite element discretization for 2D/3D MHD equations. - Jiali Xu; Haiyan Su; Zhilin Li 002 (Numer. Algorithms, 2022)

A new parameter free partially penalized immersed finite element and the optimal convergence analysis. - Haifeng Ji; Feng Wang 030; Jinru Chen; Zhilin Li 002 (Numerische Mathematik, 2022)

Numerical analysis of a free boundary problem with non-local obstacles. - Zhilin Li 002; Hayk Mikayelyan (Appl. Math. Lett., 2023)

A Neumann interface optimal control problem with elliptic PDE constraints and its discretization and numerical analysis. - Zhiyue Zhang; Kazufumi Ito; Zhilin Li 002 (CoRR, 2023)

Numerical integration rules with improved accuracy close to discontinuities. - Sergio Amat; Zhilin Li 002; Juan Ruiz-Álvarez 001; Concepcion Solano; Juan Carlos Trillo (Math. Comput. Simul., 2023)

High Order Compact Schemes for Flux Type BCs. - Zhilin Li 002; Kejia Pan (SIAM J. Sci. Comput., 2023)

Adapting Cubic Hermite Splines to the Presence of Singularities Through Correction Terms. - Sergio Amat; Zhilin Li 002; Juan Ruiz-Álvarez 001; Concepcion Solano; Juan Carlos Trillo (J. Sci. Comput., 2023)

Accurate derivatives approximations and applications to some elliptic PDEs using HOC methods. - Jin Li; Zhilin Li 002; Kejia Pan (Appl. Math. Comput., 2023)

Fully accurate approximation of piecewise smooth functions using corrected B-spline quasi-interpolants. - Zhilin Li 002; Kejia Pan; Juan Ruiz 001; Dionisio F. Yáñez (Comput. Appl. Math., 2024)

Fourth-order compact finite difference schemes for solving biharmonic equations with Dirichlet boundary conditions. - Kejia Pan; Jin Li; Zhilin Li 002; Kang Fu (CoRR, 2024)

High order compact augmented methods for Stokes equations with different boundary conditions. - Kejia Pan; Jin Li; Zhilin Li 002 (Comput. Phys. Commun., 2024)

Coupled transformation methods and analysis for BVPs on infinite domains. - Zhilin Li 002; Kejia Pan (J. Comput. Appl. Math., 2024)

Stable high order FD methods for interface and internal layer problems based on non-matching grids. - Zhilin Li 002; Kejia Pan; Juan Ruiz-Álvarez 001 (Numer. Algorithms, 2024)

A fourth order mixed compact finite difference scheme for biharmonic equations. - Kejia Pan; Jin Li; Zhilin Li 002; Hongling Hu (J. Comput. Phys., 2025)

New third-order convex splitting methods and analysis for the phase field crystal equation. - Zhijian Ye; Zhoushun Zheng; Zhilin Li 002 (Numer. Algorithms, 2025)

Analysis of harmonic average method for interface problems with discontinuous solutions and fluxes. - Kejia Pan; Hengrui Xu; Zhilin Li 002 (CoRR, 2025)