Jie Shen
Orcid: 0000-0002-4885-5732Affiliations:
- Purdue University, Department of Mathematics, West Lafayette, IN, USA
- Xiamen University, School of Mathematical Sciences, China
- Université Paris-Sud, Orsay, France (PhD 1987)
According to our database1,
Jie Shen
authored at least 153 papers
between 1994 and 2024.
Collaborative distances:
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Bibliography
2024
Higher-Order Energy-Decreasing Exponential Time Differencing Runge-Kutta methods for Gradient Flows.
CoRR, 2024
2023
An Efficient and Robust Scalar Auxialiary Variable Based Algorithm for Discrete Gradient Systems Arising from Optimizations.
SIAM J. Sci. Comput., October, 2023
Stability and Error Analysis of a Second-Order Consistent Splitting Scheme for the Navier-Stokes Equations.
SIAM J. Numer. Anal., October, 2023
J. Sci. Comput., August, 2023
Bound/positivity preserving SAV schemes for the Patlak-Keller-Segel-Navier-Stokes system.
J. Comput. Phys., May, 2023
Length Preserving Numerical Schemes for Landau-Lifshitz Equation Based on Lagrange Multiplier Approaches.
SIAM J. Sci. Comput., April, 2023
Log Orthogonal Functions in Semi-Infinite Intervals: Approximation Results and Applications.
SIAM J. Numer. Anal., February, 2023
A Fictitious Domain Spectral Method for Solving the Helmholtz Equation in Exterior Domains.
J. Sci. Comput., February, 2023
Error analysis of a fully discrete consistent splitting MAC scheme for time dependent Stokes equations.
J. Comput. Appl. Math., 2023
A positivity preserving scheme for Poisson-Nernst-Planck Navier-Stokes equations and its error analysis.
CoRR, 2023
A simple GPU implementation of spectral-element methods for solving 3D Poisson type equations on cartesian meshes.
CoRR, 2023
A simple and efficient convex optimization based bound-preserving high order accurate limiter for Cahn-Hilliard-Navier-Stokes system.
CoRR, 2023
An efficient and robust SAV based algorithm for discrete gradient systems arising from optimizations.
CoRR, 2023
Error estimate of a consistent splitting GSAV scheme for the Navier-Stokes equations.
CoRR, 2023
2022
A Fast Petrov-Galerkin Spectral Method for the Multidimensional Boltzmann Equation Using Mapped Chebyshev Functions.
SIAM J. Sci. Comput., 2022
Stability and Error Analysis of IMEX SAV Schemes for the Magneto-Hydrodynamic Equations.
SIAM J. Numer. Anal., 2022
A New Lagrange Multiplier Approach for Constructing Structure Preserving Schemes, II. Bound Preserving.
SIAM J. Numer. Anal., 2022
New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis.
Math. Comput., 2022
J. Comput. Phys., 2022
A new class of higher-order decoupled schemes for the incompressible Navier-Stokes equations and applications to rotating dynamics.
J. Comput. Phys., 2022
Bound/positivity preserving and unconditionally stable schemes for a class of fourth order nonlinear equations.
J. Comput. Phys., 2022
J. Comput. Phys., 2022
Eigenvalue Analysis and Applications of the Legendre Dual-Petrov-Galerkin Methods for Initial Value Problems.
CoRR, 2022
2021
Bound/Positivity Preserving and Energy Stable Scalar auxiliary Variable Schemes for Dissipative Systems: Applications to Keller-Segel and Poisson-Nernst-Planck Equations.
SIAM J. Sci. Comput., 2021
An Efficient Spectral Method for Elliptic PDEs in Complex Domains with Circular Embedding.
SIAM J. Sci. Comput., 2021
Stability and Error Analysis of a Class of High-Order IMEX Schemes for Navier-Stokes Equations with Periodic Boundary Conditions.
SIAM J. Numer. Anal., 2021
Unconditionally positivity preserving and energy dissipative schemes for Poisson-Nernst-Planck equations.
Numerische Mathematik, 2021
J. Sci. Comput., 2021
J. Sci. Comput., 2021
Second-Order SAV Schemes for the Nonlinear Schrödinger Equation and Their Error Analysis.
J. Sci. Comput., 2021
A bound-preserving high order scheme for variable density incompressible Navier-Stokes equations.
J. Comput. Phys., 2021
Scalar Auxiliary Variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations.
J. Comput. Phys., 2021
CoRR, 2021
A fast Petrov-Galerkin spectral method for the multi-dimensional Boltzmann equation using mapped Chebyshev functions.
CoRR, 2021
Discrete Maximum principle of a high order finite difference scheme for a generalized Allen-Cahn equation.
CoRR, 2021
Modeling and simulation of nuclear architecture reorganization process using a phase field approach.
CoRR, 2021
Implicit-explicit BDF k SAV schemes for general dissipative systems and their error analysis.
CoRR, 2021
2020
A Highly Efficient and Accurate New Scalar Auxiliary Variable Approach for Gradient Flows.
SIAM J. Sci. Comput., 2020
SIAM J. Sci. Comput., 2020
A Spectrally Accurate Approximation to Subdiffusion Equations Using the Log Orthogonal Functions.
SIAM J. Sci. Comput., 2020
Fast Fourier-like Mapped Chebyshev Spectral-Galerkin Methods for PDEs with Integral Fractional Laplacian in Unbounded Domains.
SIAM J. Numer. Anal., 2020
Unconditionally Bound Preserving and Energy Dissipative Schemes for a Class of Keller-Segel Equations.
SIAM J. Numer. Anal., 2020
SIAM J. Numer. Anal., 2020
Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows.
Numerische Mathematik, 2020
A Total Fractional-Order Variation Model for Image Super-Resolution and Its SAV Algorithm.
J. Sci. Comput., 2020
J. Sci. Comput., 2020
An Efficient and Accurate Numerical Method for the Spectral Fractional Laplacian Equation.
J. Sci. Comput., 2020
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<sup>☆</sup>.
J. Comput. Phys., 2020
Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs.
J. Comput. Phys., 2020
J. Comput. Appl. Math., 2020
Error estimate of Gauge-Uzawa methods for incompressible flows with variable density.
J. Comput. Appl. Math., 2020
On fully decoupled MSAV schemes for the Cahn-Hilliard-Navier-Stokes model of Two-Phase Incompressible Flows.
CoRR, 2020
Efficient Linear and Unconditionally Energy Stable Schemes for the Modified Phase Field Crystal Equation.
CoRR, 2020
Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation.
Adv. Comput. Math., 2020
2019
SIAM Rev., 2019
Energy stability and convergence of SAV block-centered finite difference method for gradient flows.
Math. Comput., 2019
J. Sci. Comput., 2019
Highly Efficient and Accurate Numerical Schemes for the Epitaxial Thin Film Growth Models by Using the SAV Approach.
J. Sci. Comput., 2019
Efficient SAV approach for imaginary time gradient flows with applications to one- and multi-component Bose-Einstein Condensates.
J. Comput. Phys., 2019
Stability and convergence analysis of rotational velocity correction methods for the Navier-Stokes equations.
Adv. Comput. Math., 2019
2018
Multiple Scalar Auxiliary Variable (MSAV) Approach and its Application to the Phase-Field Vesicle Membrane Model.
SIAM J. Sci. Comput., 2018
Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows.
SIAM J. Numer. Anal., 2018
Error estimates for a fully discretized scheme to a Cahn-Hilliard phase-field model for two-phase incompressible flows.
Math. Comput., 2018
Laguerre Functions and Their Applications to Tempered Fractional Differential Equations on Infinite Intervals.
J. Sci. Comput., 2018
Enriched Spectral Methods and Applications to Problems with Weakly Singular Solutions.
J. Sci. Comput., 2018
J. Comput. Phys., 2018
Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization.
J. Comput. Phys., 2018
Spectral element method with geometric mesh for two-sided fractional differential equations.
Adv. Comput. Math., 2018
2017
SIAM J. Sci. Comput., 2017
Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows.
Numerische Mathematik, 2017
Highly Accurate Pseudospectral Approximations of the Prolate Spheroidal Wave Equation for Any Bandwidth Parameter and Zonal Wavenumber.
J. Sci. Comput., 2017
Unconditionally stable Gauge-Uzawa finite element schemes for incompressible natural convection problems with variable density.
J. Comput. Phys., 2017
Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model.
J. Comput. Phys., 2017
2016
Fast Structured Direct Spectral Methods for Differential Equations with Variable Coefficients, I. The One-Dimensional Case.
SIAM J. Sci. Comput., 2016
Müntz-Galerkin Methods and Applications to Mixed Dirichlet-Neumann Boundary Value Problems.
SIAM J. Sci. Comput., 2016
Generalized Jacobi functions and their applications to fractional differential equations.
Math. Comput., 2016
Efficient Spectral-Galerkin Method and Analysis for Elliptic PDEs with Non-local Boundary Conditions.
J. Sci. Comput., 2016
A decoupled energy stable scheme for a hydrodynamic phase-field model of mixtures of nematic liquid crystals and viscous fluids.
J. Comput. Phys., 2016
Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients.
J. Comput. Phys., 2016
Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models.
J. Comput. Phys., 2016
2015
Decoupled, Energy Stable Schemes for Phase-Field Models of Two-Phase Incompressible Flows.
SIAM J. Numer. Anal., 2015
Decoupled Energy Stable Schemes for a Phase-Field Model of Two-Phase Incompressible Flows with Variable Density.
J. Sci. Comput., 2015
Efficient energy stable numerical schemes for a phase field moving contact line model.
J. Comput. Phys., 2015
A pressure correction scheme for generalized form of energy-stable open boundary conditions for incompressible flows.
J. Comput. Phys., 2015
Spectral approximation to a transmission eigenvalue problem and its applications to an inverse problem.
Comput. Math. Appl., 2015
2014
SIAM J. Sci. Comput., 2014
A new spectral method for numerical solution of the unbounded rough surface scattering problem.
J. Comput. Phys., 2014
Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains.
J. Comput. Appl. Math., 2014
2013
J. Sci. Comput., 2013
Modeling and simulations of drop pinch-off from liquid crystal filaments and the leaky liquid crystal faucet immersed in viscous fluids.
J. Comput. Phys., 2013
J. Comput. Phys., 2013
Error Analysis of the Strang Time-Splitting Laguerre-Hermite/Hermite Collocation Methods for the Gross-Pitaevskii Equation.
Found. Comput. Math., 2013
2012
Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Equations II. Unbounded Domains.
SIAM J. Sci. Comput., 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.
SIAM J. Numer. Anal., 2012
Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich-Schwoebel Type Energy: Application to Thin Film Epitaxy.
SIAM J. Numer. Anal., 2012
A New Spectral Element Method for Pricing European Options Under the Black-Scholes and Merton Jump Diffusion Models.
J. Sci. Comput., 2012
An efficient and stable spectral method for electromagnetic scattering from a layered periodic structure.
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.
J. Comput. Phys., 2012
Efficient spectral-Galerkin methods for systems of coupled second-order equations and their applications.
J. Comput. Phys., 2012
2010
Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Problems.
SIAM J. Sci. Comput., 2010
A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities.
SIAM J. Sci. Comput., 2010
Sparse Spectral Approximations of High-Dimensional Problems Based on Hyperbolic Cross.
SIAM J. Numer. Anal., 2010
Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle.
Math. Comput., 2010
A Coupled Legendre-Laguerre Spectral-Element Method for the Navier-Stokes Equations in Unbounded Domains.
J. Sci. Comput., 2010
An unconditionally stable rotational velocity-correction scheme for incompressible flows.
J. Comput. Phys., 2010
2009
A Generalized-Laguerre--Fourier--Hermite Pseudospectral Method for Computing the Dynamics of Rotating Bose--Einstein Condensates.
SIAM J. Sci. Comput., 2009
SIAM J. Numer. Anal., 2009
SIAM J. Numer. Anal., 2009
Math. Comput., 2009
J. Comput. Phys., 2009
An efficient moving mesh spectral method for the phase-field model of two-phase flows.
J. Comput. Phys., 2009
2008
SIAM J. Numer. Anal., 2008
A Laguerre-Legendre Spectral Method for the Stokes Problem in a Semi-Infinite Channel.
SIAM J. Numer. Anal., 2008
Error analysis of fully discrete velocity-correction methods for incompressible flows.
Math. Comput., 2008
Multiscale Model. Simul., 2008
A generalized-Laguerre-Hermite pseudospectral method for computing symmetric and central vortex states in Bose-Einstein condensates.
J. Comput. Phys., 2008
Irrational approximations and their applications to partial differential equations in exterior domains<sup>, </sup>.
Adv. Comput. Math., 2008
2007
Analysis of a Spectral-Galerkin Approximation to the Helmholtz Equation in Exterior Domains.
SIAM J. Numer. Anal., 2007
J. Comput. Phys., 2007
An efficient direct parallel spectral-element solver for separable elliptic problems.
J. Comput. Phys., 2007
A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering.
J. Comput. Phys., 2007
2006
SIAM J. Sci. Comput., 2006
J. Sci. Comput., 2006
Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method.
J. Comput. Phys., 2006
2005
A Fourth-Order Time-Splitting Laguerre-Hermite Pseudospectral Method for Bose-Einstein Condensates.
SIAM J. Sci. Comput., 2005
SIAM J. Numer. Anal., 2005
Error Analysis of Pressure-Correction Schemes for the Time-Dependent Stokes Equations with Open Boundary Conditions.
SIAM J. Numer. Anal., 2005
2004
SIAM J. Numer. Anal., 2004
Math. Comput., 2004
2003
A New Dual-Petrov-Galerkin Method for Third and Higher Odd-Order Differential Equations: Application to the KDV Equation.
SIAM J. Numer. Anal., 2003
SIAM J. Numer. Anal., 2003
Corrigendum: Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals.
SIAM J. Numer. Anal., 2003
Spectral and Pseudospectral Approximations Using Hermite Functions: Application to the Dirac Equation.
Adv. Comput. Math., 2003
2001
Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals.
SIAM J. Numer. Anal., 2001
2000
SIAM J. Numer. Anal., 2000
Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval.
Numerische Mathematik, 2000
A Rational Approximation and Its Applications to Differential Equations on the Half Line.
J. Sci. Comput., 2000
1999
SIAM J. Sci. Comput., 1999
1997
SIAM J. Sci. Comput., 1997
1996
On error estimates of the projection methods for the Navier-Stokes equations: Second-order schemes.
Math. Comput., 1996
1995
Efficient Spectral-Galerkin Method II. Direct Solvers of Second- and Fourth-Order Equations Using Chebyshev Polynomials.
SIAM J. Sci. Comput., 1995
1994
Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials.
SIAM J. Sci. Comput., 1994