ERROR ANALYSIS OF THE SECOND-ORDER SERENDIPITY VIRTUAL ELEMENT METHOD FOR SEMILINEAR PSEUDO-PARABOLIC EQUATIONS ON CURVED DOMAINS  

作　　者：Yang Xu Zhenguo Zhou Jingjun Zhao 

机构地区：[1]School of Mathematics,Harbin Institute of Technology,Harbin 150001,China

出　　处：《Journal of Computational Mathematics》2024年第6期1743-1776,共34页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant No.12071100);by the Fundamental Research Funds for the Central Universities(Grant No.2022FRFK060019).

摘　　要：The second-order serendipity virtual element method is studied for the semilinear pseudo-parabolic equations on curved domains in this paper.Nonhomogeneous Dirichlet boundary conditions are taken into account,the existence and uniqueness are investigated for the weak solution of the nonhomogeneous initial-boundary value problem.The Nitschebased projection method is adopted to impose the boundary conditions in a weak way.The interpolation operator is used to deal with the nonlinear term.The Crank-Nicolson scheme is employed to discretize the temporal variable.There are two main features of the proposed scheme:(i)the internal degrees of freedom are avoided no matter what type of mesh is utilized,and(ii)the Jacobian is simple to calculate when Newton’s iteration method is applied to solve the fully discrete scheme.The error estimates are established for the discrete schemes and the theoretical results are illustrated through some numerical examples.

关 键 词：Semilinear pseudo-parabolic equation Serendipity virtual element method Projection method Curved domain 

分 类 号：O17[理学—数学]