ERROR ANALYSIS OF VIRTUAL ELEMENT METHODS FOR THE TIME-DEPENDENT POISSON-NERNST-PLANCK EQUATIONS  

作　　者：Ying Yang Ya Liu Yang Liu Shi Shu 

机构地区：[1]School of Mathematics and Computational Science,Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation,Center for Applied Mathematics of Guangxi(GUET),Guilin University of Electronic Technology,Guilin 541004,China [2]School of Mathematics and Computational Science,Guilin University of Electronic Technology,Guilin 541004,China [3]School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,China

出　　处：《Journal of Computational Mathematics》2025年第3期731-770,共40页计算数学(英文)

基　　金：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).

摘　　要：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 channels.After presenting the semi-discrete scheme,the optimal H1 norm error estimates are presented for the time-dependent PNP equations,which are based on some error estimates of a virtual element energy projection.The Gummel iteration is used to decouple and linearize the PNP equations and the error analysis is also given for the iteration of fully discrete virtual element approximation.The numerical experiment on different polygonal meshes verifies the theoretical convergence results and shows the efficiency of the virtual element method.

关 键 词：Virtual element method Error estimate Poisson-Nernst-Planck equations Polygonal meshes Energy projection Gummel iteration 

分 类 号：O241.82[理学—计算数学]