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ERROR ANALYSIS OF VIRTUAL ELEMENT METHODS FOR THE TIME-DEPENDENT POISSON-NERNST-PLANCK EQUATIONS: 《Journal of Computational Mathematics》2025年第3期731-770,共40页Ying Yang Ya Liu Yang Liu Shi Shu; supported by the China NSF(NSFC 12161026);by the Special Fund for Scientific and Technological Bases and Talents of Guangxi(Grant No.Guike AD23026048);by the Guangxi Natural Science Foundation,China(Grant No.2020GXNSFAA159098);supported by the China NSF(NSFC 12371373);supported by the GUET Excellent Graduate Thesis Program(Grant No.2020YJSPYA02).; We discuss and analyze the virtual element method on general polygonal meshes for the time-dependent Poisson-Nernst-Planck(PNP)equations,which are a nonlinear coupled system widely used in semiconductors and ion chann...; 关键词：Virtual element method Error estimate Poisson-Nernst-Planck equations Polygonal meshes Energy projection Gummel iteration

TIME MULTIPOINT NONLOCAL PROBLEM FOR A STOCHASTIC SCHRÖDINGER EQUATION: 《Journal of Computational Mathematics》2025年第2期369-393,共25页Roger Pettersson Ali Sirma Tarkan Aydin; A time multipoint nonlocal problem for a Schrödinger equation driven by a cylindrical Q-Wiener process is presented.The initial value depends on a finite number of future values.Existence and uniqueness of a solution ...; 关键词：Time nonlocal problem Mild solution Cylindrical Wiener process Time discretization Abstract time-dependent stochastic Schrödinger equation Euler-Maruyama method

UNIFORM SUPERCONVERGENCE ANALYSIS OF A TWO-GRID MIXED FINITE ELEMENT METHOD FOR THE TIME-DEPENDENT BI-WAVE PROBLEM MODELING D-WAVE SUPERCONDUCTORS: 《Journal of Computational Mathematics》2024年第2期415-431,共17页Yanmi Wu Dongyang Shi; supported by the National Natural Science Foundation of China(Grant Nos.12201640,12071443).; In this paper,a two-grid mixed finite element method(MFEM)of implicit Backward Euler(BE)formula is presented for the fourth order time-dependent singularly perturbed Bi-wave problem for d-wave superconductors by the n...; 关键词：Time-dependent Bi-wave problem Two-grid mixed finite element method Uniform superclose and superconvergent estimates

STRONG CONVERGENCE OF THE EULER-MARUYAMA METHOD FOR NONLINEAR STOCHASTIC VOLTERRA INTEGRAL EQUATIONS WITH TIME-DEPENDENT DELAY: 《Journal of Computational Mathematics》2022年第3期437-452,共16页Siyuan Qi Guangqiang Lan; Supported by Beijing Municipal Natural Science Foundation(1192013).; We consider a nonlinear stochastic Volterra integral equation with time-dependent delay and the corresponding Euler-Maruyama method in this paper.Strong convergence rate(at fixed point)of the corresponding Euler-Maruy...; 关键词：Stochastic Volterra integral equation Euler-Maruyama method Strong convergence Time-dependent delay

UNCONDITIONALLY OPTIMAL ERROR ESTIMATES OF THE BILINEAR-CONSTANT SCHEME FOR TIME-DEPENDENT NAVIER-STOKES EQUATIONS: 《Journal of Computational Mathematics》2022年第1期127-146,共20页Huaijun Yang Dongyang Shi; supported by National Natural Science Foundation of China(No.11671369);the Doctoral Starting Foundation of Zhengzhou University of Aeronautics(No.63020390).; In this paper,the unconditional error estimates are presented for the time-dependent Navier-Stokes equations by the bilinear-constant scheme.The corresponding optimal error estimates for the velocity and the pressure ...; 关键词：Navier-Stokes equations Unconditionally optimal error estimates Bilinear-constant scheme Time-discrete system.

A HYBRID EXPLICIT-IMPLICIT SCHEME FOR THE TIME-DEPENDENT WIGNER EQUATION: 《Journal of Computational Mathematics》2021年第1期22-42,共21页Haiyan Jiang Tiao Lu Xu Yin; This research was supported in part by the NSFC(91434201,91630130,11671038,11421101).; This paper designs a hybrid scheme based on finite difference methods and a spectral method for the time-dependent Wigner equation,and gives the error analysis for the full discret ization of its initial value problem...; 关键词：Finite diference method Spectral method Hybrid scheme Error analysis Wigner equation.

SUPERCONVERGENCE ANALYSIS OF LOW ORDER NONCONFORMING MIXED FINITE ELEMENT METHODS FOR TIME-DEPENDENT NAVIER-STOKES EQUATIONS: 《Journal of Computational Mathematics》2021年第1期63-80,共18页Huaijun Yang Dongyang Shi Qian Liu; This work is supported by National Natural Science Foundation of China(Nos.11671369,11271340).; In this paper,the superconvergence properties of the time-dependent Navier-Stokes equations are investigated by a low order nonconforming mixed finite element method(MFEM).In terms of the integral identity technique,t...; 关键词：Navier-Stokes equations Nonconforming MFEM Supercloseness and super-convergence.

LOCAL ANALYSIS OF THE FULLY DISCRETE LOCAL DISCONTINUOUS GALERKIN METHOD FOR THE TIME-DEPENDENT SINGULARLY PERTURBED PROBLEM被引量：1: 《Journal of Computational Mathematics》2017年第3期265-288,共24页Yao Cheng Qiang Zhang; In this paper we consider the fully discrete local discontinuous Galerkin method, where the third order explicit Runge-Kutta time marching is coupled. For the one-dimensional time-dependent singularly perturbed proble...; 关键词：Local analysis Runge-Kutta method Local discontinuous Galerkin method Singularly perturbed problem Boundary layer

A NEW PRECONDITIONING STRATEGY FOR SOLVING A CLASS OF TIME-DEPENDENT PDE-CONSTRAINED OPTIMIZATION PROBLEMS被引量：2: 《Journal of Computational Mathematics》2014年第3期215-232,共18页Minli Zeng Guofeng Zhang; The work was supported by the National Natural Science Foundation of China （11271174）. The authors would like to thank the referees for the comments and constructive suggestions, which are valuable in improving the quality of the manuscript.; In this paper, by exploiting the special block and sparse structure of the coefficient matrix, we present a new preconditioning strategy for solving large sparse linear systems arising in the time-dependent distribute...; 关键词：PDE-constrained optimization Reduced linear system of equations PRECONDITIONING Saddle point problem Krylov subspace methods.

A SECOND ORDER MODIFIED CHARACTERISTICS VARIATIONAL MULTISCALE FINITE ELEMENT METHOD FOR TIME-DEPENDENT NAVIER-STOKES PROBLEMS: 《Journal of Computational Mathematics》2013年第2期154-174,共21页Zhiyong Si Jian Su Yinnian He; In this paper, by combining the second order characteristics time discretization with the variational multiscale finite element method in space we get a second order modified characteristics variational multiscale fin...; 关键词：Modified method of characteristics Defect-correction finite element method Navier-Stokes problems Characteristics-based method Lid-driven problem.

TIME-DEPENDENT