Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials. - Jie Shen 001 (SIAM J. Sci. Comput., 1994)

Efficient Spectral-Galerkin Method II. Direct Solvers of Second- and Fourth-Order Equations Using Chebyshev Polynomials. - Jie Shen 001 (SIAM J. Sci. Comput., 1995)

On error estimates of the projection methods for the Navier-Stokes equations: Second-order schemes. - Jie Shen 001 (Math. Comput., 1996)

Efficient Spectral-Galerkin Methods III: Polar and Cylindrical Geometries. - Jie Shen 001 (SIAM J. Sci. Comput., 1997)

Efficient Spectral-Galerkin Methods IV. Spherical Geometries. - Jie Shen 001 (SIAM J. Sci. Comput., 1999)

A Rational Approximation and Its Applications to Differential Equations on the Half Line. - Ben-yu Guo; Jie Shen 001; Zhong-Qing Wang (J. Sci. Comput., 2000)

Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval. - Ben-yu Guo; Jie Shen 001 (Numerische Mathematik, 2000)

Stable and Efficient Spectral Methods in Unbounded Domains Using Laguerre Functions. - Jie Shen 001 (SIAM J. Numer. Anal., 2000)

Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals. - Qiang Du 001; Ben-yu Guo; Jie Shen 001 (SIAM J. Numer. Anal., 2001)

Spectral and Pseudospectral Approximations Using Hermite Functions: Application to the Dirac Equation. - Ben-yu Guo; Jie Shen 001; Cheng-long Xu (Adv. Comput. Math., 2003)

Corrigendum: Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals. - Qiang Du 001; Ben-yu Guo; Jie Shen 001 (SIAM J. Numer. Anal., 2003)

Velocity-Correction Projection Methods for Incompressible Flows. - Jean-Luc Guermond; Jie Shen 001 (SIAM J. Numer. Anal., 2003)

A New Dual-Petrov-Galerkin Method for Third and Higher Odd-Order Differential Equations: Application to the KDV Equation. - Jie Shen 001 (SIAM J. Numer. Anal., 2003)

On the error estimates for the rotational pressure-correction projection methods. - Jean-Luc Guermond; Jie Shen 001 (Math. Comput., 2004)

Error Analysis for Mapped Legendre Spectral and Pseudospectral Methods. - Jie Shen 001; Li-lian Wang (SIAM J. Numer. Anal., 2004)

Error Analysis for Mapped Jacobi Spectral Methods. - Li-lian Wang; Jie Shen 001 (J. Sci. Comput., 2005)

Error Analysis of Pressure-Correction Schemes for the Time-Dependent Stokes Equations with Open Boundary Conditions. - Jean-Luc Guermond; Peter D. Minev; Jie Shen 001 (SIAM J. Numer. Anal., 2005)

Spectral Approximation of the Helmholtz Equation with High Wave Numbers. - Jie Shen 001; Li-lian Wang (SIAM J. Numer. Anal., 2005)

A Fourth-Order Time-Splitting Laguerre-Hermite Pseudospectral Method for Bose-Einstein Condensates. - Weizhu Bao; Jie Shen 001 (SIAM J. Sci. Comput., 2005)

Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method. - Xiaofeng Yang 003; James J. Feng; Chun Liu 009; Jie Shen 001 (J. Comput. Phys., 2006)

Optimal Spectral-Galerkin Methods Using Generalized Jacobi Polynomials. - Ben-yu Guo; Jie Shen 001; Li-lian Wang (J. Sci. Comput., 2006)

A Stable High-Order Method for Two-Dimensional Bounded-Obstacle Scattering. - David P. Nicholls; Jie Shen 001 (SIAM J. Sci. Comput., 2006)

A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering. - Qirong Fang; David P. Nicholls; Jie Shen 001 (J. Comput. Phys., 2007)

An efficient direct parallel spectral-element solver for separable elliptic problems. - Yuen-Yick Kwan; Jie Shen 001 (J. Comput. Phys., 2007)

Gauge-Uzawa methods for incompressible flows with variable density. - Jae-Hong Pyo; Jie Shen 001 (J. Comput. Phys., 2007)

Analysis of a Spectral-Galerkin Approximation to the Helmholtz Equation in Exterior Domains. - Jie Shen 001; Li-lian Wang (SIAM J. Numer. Anal., 2007)

Irrational approximations and their applications to partial differential equations in exterior domains, . - Ben-yu Guo; Jie Shen 001 (Adv. Comput. Math., 2008)

A generalized-Laguerre-Hermite pseudospectral method for computing symmetric and central vortex states in Bose-Einstein condensates. - Weizhu Bao; Jie Shen 001 (J. Comput. Phys., 2008)

A Dual-Petrov-Galerkin Method for the Kawahara-Type Equations. - Juan-Ming Yuan; Jie Shen 001; Jiahong Wu (J. Sci. Comput., 2008)

Dimensional Robustness and Instability of Sheared, Semidilute, Nanorod Dispersions. - Xiaofeng Yang 003; Zhenlu Cui; M. Gregory Forest; Qi Wang 021; Jie Shen 001 (Multiscale Model. Simul., 2008)

Error analysis of fully discrete velocity-correction methods for incompressible flows. - Jean-Luc Guermond; Jie Shen 001; Xiaofeng Yang 003 (Math. Comput., 2008)

A Laguerre-Legendre Spectral Method for the Stokes Problem in a Semi-Infinite Channel. - Mejdi Azaïez; Jie Shen 001; Chuanju Xu; Qingqu Zhuang (SIAM J. Numer. Anal., 2008)

On Numerical Approximations of Forward-Backward Stochastic Differential Equations. - Jin Ma; Jie Shen 001; Yanhong Zhao (SIAM J. Numer. Anal., 2008)

An efficient moving mesh spectral method for the phase-field model of two-phase flows. - Jie Shen 001; Xiaofeng Yang 003 (J. Comput. Phys., 2009)

Efficient stochastic Galerkin methods for random diffusion equations. - Dongbin Xiu; Jie Shen 001 (J. Comput. Phys., 2009)

On spectral approximations in elliptical geometries using Mathieu functions. - Jie Shen 001; Li-lian Wang (Math. Comput., 2009)

A Rigorous Numerical Analysis of the Transformed Field Expansion Method. - David P. Nicholls; Jie Shen 001 (SIAM J. Numer. Anal., 2009)

A Triangular Spectral Element Method Using Fully Tensorial Rational Basis Functions. - Jie Shen 001; Li-lian Wang; Huiyuan Li (SIAM J. Numer. Anal., 2009)

A Generalized-Laguerre–Fourier–Hermite Pseudospectral Method for Computing the Dynamics of Rotating Bose–Einstein Condensates. - Weizhu Bao; Hailiang Li; Jie Shen 001 (SIAM J. Sci. Comput., 2009)

An unconditionally stable rotational velocity-correction scheme for incompressible flows. - Suchuan Dong; Jie Shen 001 (J. Comput. Phys., 2010)

A Coupled Legendre-Laguerre Spectral-Element Method for the Navier-Stokes Equations in Unbounded Domains. - Qingqu Zhuang; Jie Shen 001; Chuanju Xu (J. Sci. Comput., 2010)

Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle. - Huiyuan Li; Jie Shen 001 (Math. Comput., 2010)

Sparse Spectral Approximations of High-Dimensional Problems Based on Hyperbolic Cross. - Jie Shen 001; Li-lian Wang (SIAM J. Numer. Anal., 2010)

A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities. - Jie Shen 001; Xiaofeng Yang 003 (SIAM J. Sci. Comput., 2010)

Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Problems. - Jie Shen 001; Haijun Yu (SIAM J. Sci. Comput., 2010)

Efficient spectral-Galerkin methods for systems of coupled second-order equations and their applications. - Feng Chen 034; Jie Shen 001 (J. Comput. Phys., 2012)

A time-stepping scheme involving constant coefficient matrices for phase-field simulations of two-phase incompressible flows with large density ratios. - Suchuan Dong; Jie Shen 001 (J. Comput. Phys., 2012)

An efficient and stable spectral method for electromagnetic scattering from a layered periodic structure. - Ying He 007; David P. Nicholls; Jie Shen 001 (J. Comput. Phys., 2012)

A New Spectral Element Method for Pricing European Options Under the Black-Scholes and Merton Jump Diffusion Models. - Feng Chen 034; Jie Shen 001; Haijun Yu (J. Sci. Comput., 2012)

Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich-Schwoebel Type Energy: Application to Thin Film Epitaxy. - Jie Shen 001; Cheng Wang 015; Xiaoming Wang 009; Steven M. Wise (SIAM J. Numer. Anal., 2012)

On the Approximation of the Fokker-Planck Equation of the Finitely Extensible Nonlinear Elastic Dumbbell Model I: A New Weighted Formulation and an Optimal Spectral-Galerkin Algorithm in Two Dimensions. - Jie Shen 001; Haijun Yu (SIAM J. Numer. Anal., 2012)

Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Equations II. Unbounded Domains. - Jie Shen 001; Haijun Yu (SIAM J. Sci. Comput., 2012)

Error Analysis of the Strang Time-Splitting Laguerre-Hermite/Hermite Collocation Methods for the Gross-Pitaevskii Equation. - Jie Shen 001; Zhong-Qing Wang (Found. Comput. Math., 2013)

A GPU parallelized spectral method for elliptic equations in rectangular domains. - Feng Chen 034; Jie Shen 001 (J. Comput. Phys., 2013)

Modeling and simulations of drop pinch-off from liquid crystal filaments and the leaky liquid crystal faucet immersed in viscous fluids. - Xiaofeng Yang 003; M. Gregory Forest; Huiyuan Li; Chun Liu 009; Jie Shen 001; Qi Wang 021; Falai Chen (J. Comput. Phys., 2013)

A Spectral-Element Method for Transmission Eigenvalue Problems. - Jing An; Jie Shen 001 (J. Sci. Comput., 2013)

Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains. - Jie Shen 001; Li-Lian Wang; Haijun Yu (J. Comput. Appl. Math., 2014)

A new spectral method for numerical solution of the unbounded rough surface scattering problem. - Ying He 007; Peijun Li; Jie Shen 001 (J. Comput. Phys., 2014)

Decoupled Energy Stable Schemes for Phase-Field Models of Two-Phase Complex Fluids. - Jie Shen 001; Xiaofeng Yang 003 (SIAM J. Sci. Comput., 2014)

Spectral approximation to a transmission eigenvalue problem and its applications to an inverse problem. - Jing An; Jie Shen 001 (Comput. Math. Appl., 2015)

A pressure correction scheme for generalized form of energy-stable open boundary conditions for incompressible flows. - Suchuan Dong; Jie Shen 001 (J. Comput. Phys., 2015)

Efficient energy stable numerical schemes for a phase field moving contact line model. - Jie Shen 001; Xiaofeng Yang 003; Haijun Yu (J. Comput. Phys., 2015)

Decoupled Energy Stable Schemes for a Phase-Field Model of Two-Phase Incompressible Flows with Variable Density. - Chun Liu 009; Jie Shen 001; Xiaofeng Yang 003 (J. Sci. Comput., 2015)

Dynamic Transitions of Quasi-geostrophic Channel Flow. - Henk Dijkstra; Taylan Sengul; Jie Shen 001; Shouhong Wang (SIAM J. Appl. Math., 2015)

Decoupled, Energy Stable Schemes for Phase-Field Models of Two-Phase Incompressible Flows. - Jie Shen 001; Xiaofeng Yang 003 (SIAM J. Numer. Anal., 2015)

Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models. - Ying Chen; Jie Shen 001 (J. Comput. Phys., 2016)

Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients. - Zhiping Mao; Jie Shen 001 (J. Comput. Phys., 2016)

A decoupled energy stable scheme for a hydrodynamic phase-field model of mixtures of nematic liquid crystals and viscous fluids. - Jia Zhao 004; Xiaofeng Yang 003; Jie Shen 001; Qi Wang 021 (J. Comput. Phys., 2016)

Efficient Spectral-Galerkin Method and Analysis for Elliptic PDEs with Non-local Boundary Conditions. - Lina Hu; Lina Ma; Jie Shen 001 (J. Sci. Comput., 2016)

Generalized Jacobi functions and their applications to fractional differential equations. - Sheng Chen; Jie Shen 001; Li-Lian Wang (Math. Comput., 2016)

Müntz-Galerkin Methods and Applications to Mixed Dirichlet-Neumann Boundary Value Problems. - Jie Shen 001; Yingwei Wang 001 (SIAM J. Sci. Comput., 2016)

Fast Structured Direct Spectral Methods for Differential Equations with Variable Coefficients, I. The One-Dimensional Case. - Jie Shen 001; Yingwei Wang 001; Jianlin Xia (SIAM J. Sci. Comput., 2016)

Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model. - Qing Cheng 003; Xiaofeng Yang 003; Jie Shen 001 (J. Comput. Phys., 2017)

Unconditionally stable Gauge-Uzawa finite element schemes for incompressible natural convection problems with variable density. - Jilian Wu; Jie Shen 001; Xinlong Feng (J. Comput. Phys., 2017)

Highly Accurate Pseudospectral Approximations of the Prolate Spheroidal Wave Equation for Any Bandwidth Parameter and Zonal Wavenumber. - H. Alici; Jie Shen 001 (J. Sci. Comput., 2017)

Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows. - Yongyong Cai; Heejun Choi; Jie Shen 001 (Numerische Mathematik, 2017)

Hermite Spectral Methods for Fractional PDEs in Unbounded Domains. - Zhiping Mao; Jie Shen 001 (SIAM J. Sci. Comput., 2017)

Spectral element method with geometric mesh for two-sided fractional differential equations. - Zhiping Mao; Jie Shen 001 (Adv. Comput. Math., 2018)

Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization. - Ying Chen; John S. Lowengrub; Jie Shen 001; Cheng Wang 015; Steven M. Wise (J. Comput. Phys., 2018)

The scalar auxiliary variable (SAV) approach for gradient flows. - Jie Shen 001; Jie Xu 033; Jiang Yang (J. Comput. Phys., 2018)

Enriched Spectral Methods and Applications to Problems with Weakly Singular Solutions. - Sheng Chen; Jie Shen 001 (J. Sci. Comput., 2018)

Laguerre Functions and Their Applications to Tempered Fractional Differential Equations on Infinite Intervals. - Sheng Chen; Jie Shen 001; Li-Lian Wang (J. Sci. Comput., 2018)

Approximations on SO(3) by Wigner D-matrix and Applications. - Jie Shen 001; Jie Xu 033; Pingwen Zhang (J. Sci. Comput., 2018)

Error estimates for a fully discretized scheme to a Cahn-Hilliard phase-field model for two-phase incompressible flows. - Yongyong Cai; Jie Shen 001 (Math. Comput., 2018)

Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows. - Jie Shen 001; Jie Xu 033 (SIAM J. Numer. Anal., 2018)

Multiple Scalar Auxiliary Variable (MSAV) Approach and its Application to the Phase-Field Vesicle Membrane Model. - Qing Cheng 003; Jie Shen 001 (SIAM J. Sci. Comput., 2018)

Stability and convergence analysis of rotational velocity correction methods for the Navier-Stokes equations. - Feng Chen 019; Jie Shen 001 (Adv. Comput. Math., 2019)

A new Lagrange Multiplier approach for gradient flows. - Qing Cheng 003; Chun Liu 009; Jie Shen 001 (CoRR, 2019)

Global constraints preserving SAV schemes for gradient flows. - Qing Cheng 003; Jie Shen 001 (CoRR, 2019)

Efficient SAV approach for imaginary time gradient flows with applications to one- and multi-component Bose-Einstein Condensates. - Qingqu Zhuang; Jie Shen 001 (J. Comput. Phys., 2019)

Highly Efficient and Accurate Numerical Schemes for the Epitaxial Thin Film Growth Models by Using the SAV Approach. - Qing Cheng 003; Jie Shen 001; Xiaofeng Yang 003 (J. Sci. Comput., 2019)

An Efficient Space-Time Method for Time Fractional Diffusion Equation. - Jie Shen 001; Chang-Tao Sheng (J. Sci. Comput., 2019)

Energy stability and convergence of SAV block-centered finite difference method for gradient flows. - Xiaoli Li 008; Jie Shen 001; Hongxing Rui (Math. Comput., 2019)

Fast structured Jacobi-Jacobi transforms. - Jie Shen 001; Yingwei Wang 001; Jianlin Xia (Math. Comput., 2019)

A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows. - Jie Shen 001; Jie Xu 033; Jiang Yang (SIAM Rev., 2019)

Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation. - Xiaoli Li 008; Jie Shen 001 (Adv. Comput. Math., 2020)

Log orthogonal functions: approximation properties and applications. - Sheng Chen; Jie Shen 001 (CoRR, 2020)

Efficient Linear and Unconditionally Energy Stable Schemes for the Modified Phase Field Crystal Equation. - Xiaoli Li 008; Jie Shen 001 (CoRR, 2020)

On fully decoupled MSAV schemes for the Cahn-Hilliard-Navier-Stokes model of Two-Phase Incompressible Flows. - Xiaoli Li 008; Jie Shen 001 (CoRR, 2020)

Error estimate of Gauge-Uzawa methods for incompressible flows with variable density. - Hongtao Chen; Jingjing Mao; Jie Shen 001 (J. Comput. Appl. Math., 2020)

An efficient numerical scheme for a 3D spherical dynamo equation. - Ting Cheng; Lina Ma; Jie Shen 001 (J. Comput. Appl. Math., 2020)

Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs. - Jiaxiang Cai; Jie Shen 001 (J. Comput. Phys., 2020)

A new interface capturing method for Allen-Cahn type equations based on a flow dynamic approach in Lagrangian coordinates, I. One-dimensional case☆. - Qing Cheng 003; Chun Liu 009; Jie Shen 001 (J. Comput. Phys., 2020)

Bound preserving and energy dissipative schemes for porous medium equation. - Yiqi Gu; Jie Shen 001 (J. Comput. Phys., 2020)

An Efficient and Accurate Numerical Method for the Spectral Fractional Laplacian Equation. - Sheng Chen; Jie Shen 001 (J. Sci. Comput., 2020)

Accurate and Efficient Spectral Methods for Elliptic PDEs in Complex Domains. - Yiqi Gu; Jie Shen 001 (J. Sci. Comput., 2020)

A Total Fractional-Order Variation Model for Image Super-Resolution and Its SAV Algorithm. - Wenjuan Yao; Jie Shen 001; Zhichang Guo; Jiebao Sun; Boying Wu (J. Sci. Comput., 2020)

Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows. - Hongtao Chen; Jingjing Mao; Jie Shen 001 (Numerische Mathematik, 2020)

Error Analysis of the SAV-MAC Scheme for the Navier-Stokes Equations. - Xiaoli Li 008; Jie Shen 001 (SIAM J. Numer. Anal., 2020)

Unconditionally Bound Preserving and Energy Dissipative Schemes for a Class of Keller-Segel Equations. - Jie Shen 001; Jie Xu 033 (SIAM J. Numer. Anal., 2020)

Fast Fourier-like Mapped Chebyshev Spectral-Galerkin Methods for PDEs with Integral Fractional Laplacian in Unbounded Domains. - Changtao Sheng; Jie Shen 001; Tao Tang 003; Li-Lian Wang; Huifang Yuan (SIAM J. Numer. Anal., 2020)

A Spectrally Accurate Approximation to Subdiffusion Equations Using the Log Orthogonal Functions. - Sheng Chen; Jie Shen 001; Zhimin Zhang 002; Zhi Zhou 002 (SIAM J. Sci. Comput., 2020)

Global Constraints Preserving Scalar Auxiliary Variable Schemes for Gradient Flows. - Qing Cheng 003; Jie Shen 001 (SIAM J. Sci. Comput., 2020)

A Highly Efficient and Accurate New Scalar Auxiliary Variable Approach for Gradient Flows. - Fukeng Huang; Jie Shen 001; Zhiguo Yang (SIAM J. Sci. Comput., 2020)

Implicit-explicit BDF k SAV schemes for general dissipative systems and their error analysis. - Fukeng Huang; Jie Shen 001 (CoRR, 2021)

Modeling and simulation of nuclear architecture reorganization process using a phase field approach. - Qing Cheng 003; Pourya Delafrouz; Jie Liang 002; Chun Liu 009; Jie Shen 001 (CoRR, 2021)

Discrete Maximum principle of a high order finite difference scheme for a generalized Allen-Cahn equation. - Jie Shen 001; Xiangxiong Zhang (CoRR, 2021)

A fast Petrov-Galerkin spectral method for the multi-dimensional Boltzmann equation using mapped Chebyshev functions. - Jingwei Hu; Xiaodong Huang; Jie Shen 001; Haizhao Yang (CoRR, 2021)

A new Lagrange multiplier approach for constructing positivity preserving schemes. - Qing Cheng 003; Jie Shen 001 (CoRR, 2021)

Generalized SAV approaches for gradient systems. - Qing Cheng 003; Chun Liu 009; Jie Shen 001 (J. Comput. Appl. Math., 2021)

Scalar Auxiliary Variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations. - Xavier Antoine; Jie Shen 001; Qinglin Tang (J. Comput. Phys., 2021)

Computing interface with quasiperiodicity. - Duo Cao; Jie Shen 001; Jie Xu 033 (J. Comput. Phys., 2021)

A bound-preserving high order scheme for variable density incompressible Navier-Stokes equations. - Maojun Li; Yongping Cheng; Jie Shen 001; Xiangxiong Zhang (J. Comput. Phys., 2021)

Second-Order SAV Schemes for the Nonlinear Schrödinger Equation and Their Error Analysis. - Beichuan Deng; Jie Shen 001; Qingqu Zhuang (J. Sci. Comput., 2021)

Efficient Spectral Methods for PDEs with Spectral Fractional Laplacian. - Changtao Sheng; Duo Cao; Jie Shen 001 (J. Sci. Comput., 2021)

Efficient Structure Preserving Schemes for the Klein-Gordon-Schrödinger Equations. - Yanrong Zhang; Jie Shen 001 (J. Sci. Comput., 2021)

Unconditionally positivity preserving and energy dissipative schemes for Poisson-Nernst-Planck equations. - Jie Shen 001; Jie Xu 033 (Numerische Mathematik, 2021)

Stability and Error Analysis of a Class of High-Order IMEX Schemes for Navier-Stokes Equations with Periodic Boundary Conditions. - Fukeng Huang; Jie Shen 001 (SIAM J. Numer. Anal., 2021)

An Efficient Spectral Method for Elliptic PDEs in Complex Domains with Circular Embedding. - Yiqi Gu; Jie Shen 001 (SIAM J. Sci. Comput., 2021)

Bound/Positivity Preserving and Energy Stable Scalar auxiliary Variable Schemes for Dissipative Systems: Applications to Keller-Segel and Poisson-Nernst-Planck Equations. - Fukeng Huang; Jie Shen 001 (SIAM J. Sci. Comput., 2021)

Modeling and simulation of cell nuclear architecture reorganization process. - Qing Cheng 003; Pourya Delafrouz; Jie Liang 002; Chun Liu 009; Jie Shen 001 (J. Comput. Phys., 2022)

Bound/positivity preserving and unconditionally stable schemes for a class of fourth order nonlinear equations. - Fukeng Huang; Jie Shen 001; Ke Wu (J. Comput. Phys., 2022)

A new class of higher-order decoupled schemes for the incompressible Navier-Stokes equations and applications to rotating dynamics. - Ke Wu; Fukeng Huang; Jie Shen 001 (J. Comput. Phys., 2022)

A generalized SAV approach with relaxation for dissipative systems. - Yanrong Zhang; Jie Shen 001 (J. Comput. Phys., 2022)

New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis. - Xiaoli Li 008; Jie Shen 001; Zhengguang Liu (Math. Comput., 2022)

A New Lagrange Multiplier Approach for Constructing Structure Preserving Schemes, II. Bound Preserving. - Qing Cheng 003; Jie Shen 001 (SIAM J. Numer. Anal., 2022)

Stability and Error Analysis of IMEX SAV Schemes for the Magneto-Hydrodynamic Equations. - Xiaoli Li 008; Weilong Wang; Jie Shen 001 (SIAM J. Numer. Anal., 2022)

A Fast Petrov-Galerkin Spectral Method for the Multidimensional Boltzmann Equation Using Mapped Chebyshev Functions. - Jingwei Hu; Xiaodong Huang; Jie Shen 001; Haizhao Yang (SIAM J. Sci. Comput., 2022)

Error estimate of a consistent splitting GSAV scheme for the Navier-Stokes equations. - Xiaoli Li 008; Jie Shen 001 (CoRR, 2023)

An efficient and robust SAV based algorithm for discrete gradient systems arising from optimizations. - Xinyu Liu; Jie Shen 001; Xiangxiong Zhang (CoRR, 2023)

An Element-wise RSAV Algorithm for Unconstrained Optimization Problems. - Shiheng Zhang; Jiahao Zhang 002; Jie Shen 001; Guang Lin 001 (CoRR, 2023)

A simple GPU implementation of spectral-element methods for solving 3D Poisson type equations on cartesian meshes. - Xinyu Liu; Jie Shen 001; Xiangxiong Zhang (CoRR, 2023)

Global error estimates of high-order fully decoupled schemes for the Cahn-Hilliard-Navier-Stokes model of Two-Phase Incompressible Flows. - Xiaoli Li 008; Nan Zheng; Jie Shen 001; Zhengguang Liu (CoRR, 2023)

A positivity preserving scheme for Poisson-Nernst-Planck Navier-Stokes equations and its error analysis. - Ziyao Yu; Qing Cheng 003; Jie Shen 001; Changyou Wang (CoRR, 2023)

Error analysis of a fully discrete consistent splitting MAC scheme for time dependent Stokes equations. - Xiaoli Li 008; Jie Shen 001 (J. Comput. Appl. Math., 2023)

A Fictitious Domain Spectral Method for Solving the Helmholtz Equation in Exterior Domains. - Yiqi Gu; Jie Shen 001 (J. Sci. Comput., 2023)

Log Orthogonal Functions in Semi-Infinite Intervals: Approximation Results and Applications. - Sheng Chen; Jie Shen 001 (SIAM J. Numer. Anal., 2023)

Length Preserving Numerical Schemes for Landau-Lifshitz Equation Based on Lagrange Multiplier Approaches. - Qing Cheng 003; Jie Shen 001 (SIAM J. Sci. Comput., 2023)

Bound/positivity preserving SAV schemes for the Patlak-Keller-Segel-Navier-Stokes system. - Xueling Huang; Jie Shen 001 (J. Comput. Phys., 2023)

A Ginzburg-Landau-H-1 Model and Its SAV Algorithm for Image Inpainting. - Xiangyu Bai; Jiebao Sun; Jie Shen 001; Wenjuan Yao; Zhichang Guo (J. Sci. Comput., 2023)

Stability and Error Analysis of a Second-Order Consistent Splitting Scheme for the Navier-Stokes Equations. - Fukeng Huang; Jie Shen 001 (SIAM J. Numer. Anal., 2023)

An Efficient and Robust Scalar Auxialiary Variable Based Algorithm for Discrete Gradient Systems Arising from Optimizations. - Xinyu Liu; Jie Shen 001; Xiangxiong Zhang (SIAM J. Sci. Comput., 2023)

Higher-Order Energy-Decreasing Exponential Time Differencing Runge-Kutta methods for Gradient Flows. - Zhaohui Fu; Jie Shen 001; Jiang Yang (CoRR, 2024)

On a class of higher-order length preserving and energy decreasing IMEX schemes for the Landau-Lifshitz equation. - Xiaoli Li 008; Nan Zheng; Jie Shen 001 (CoRR, 2024)

Efficient energy stable numerical schemes for Cahn-Hilliard equations with dynamical boundary conditions. - Xinyu Liu; Jie Shen 001; Nan Zheng (J. Comput. Phys., 2024)

Efficient and stable SAV-based methods for gradient flows arising from deep learning. - Ziqi Ma; Zhiping Mao; Jie Shen 001 (J. Comput. Phys., 2024)

On a New Class of BDF and IMEX Schemes for Parabolic Type Equations. - Fukeng Huang; Jie Shen 001 (SIAM J. Numer. Anal., 2024)

A Simple and Efficient Convex Optimization Based Bound-Preserving High Order Accurate Limiter for Cahn-Hilliard-Navier-Stokes System. - Chen Liu 015; Beatrice Riviere; Jie Shen 001; Xiangxiong Zhang (SIAM J. Sci. Comput., 2024)

Energy-dissipative evolutionary deep operator neural networks. - Jiahao Zhang 002; Shiheng Zhang; Jie Shen 001; Guang Lin 001 (J. Comput. Phys., 2024)

Eigenvalue analysis and applications of the Legendre dual-Petrov-Galerkin methods for initial value problems. - Desong Kong; Jie Shen 001; Li-Lian Wang; Shuhuang Xiang (Adv. Comput. Math., 2024)

Stability and error analysis of linear IMEX schemes for sixth-order Cahn-Hilliard-type equations. - Nan Zheng; Jie Shen 001 (Commun. Nonlinear Sci. Numer. Simul., 2025)

A Relaxed Vector Auxiliary Variable Algorithm for Unconstrained Optimization Problems. - Shiheng Zhang; Jiahao Zhang 002; Jie Shen 001; Guang Lin 001 (SIAM J. Sci. Comput., 2025)

Numerical analysis of a semi-implicit Euler scheme for the Keller-Segel model. - Xueling Huang; Olivier Goubet; Jie Shen 001 (CoRR, 2025)

On a Class of Higher-Order Fully Decoupled Schemes for the Cahn-Hilliard-Navier-Stokes System. - Xiaoli Li 008; Zhengguang Liu; Jie Shen 001; Nan Zheng (J. Sci. Comput., 2025)

Stability and error analysis of a new class of higher-order consistent splitting schemes for the Navier-Stokes equations. - Fukeng Huang; Jie Shen 001 (CoRR, 2025)