Semi-Discrete and Fully Discrete Weak Galerkin Finite Element Methods for a Quasistatic Maxwell Viscoelastic Model  

作　　者：Jihong Xiao Zimo Zhu Xiaoping Xie 

机构地区：[1]School of Mathematics,Sichuan University,Chengdu 610064,China [2]Mathematics Department of Jinjiang College,Sichuan University,Pengshan 620860,China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2023年第1期79-110,共32页高等学校计算数学学报（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No.12171340).

摘　　要：This paper considers weak Galerkin finite element approximations on polygonal/polyhedral meshes for a quasistatic Maxwell viscoelastic model.The spatial discretization uses piecewise polynomials of degree k(k≥1)for the stress approximation,degree k+1 for the velocity approximation,and degree k for the numerical trace of velocity on the inter-element boundaries.The temporal discretization in the fully discrete method adopts a backward Euler difference scheme.We show the existence and uniqueness of the semi-discrete and fully discrete solutions,and derive optimal a priori error estimates.Numerical examples are provided to support the theoretical analysis.

关 键 词：Quasistatic Maxwell viscoelastic model weak Galerkin method semi-discrete scheme fully discrete scheme error estimate 

分 类 号：O241.82[理学—计算数学]