Semi-Discrete and Fully Discrete Weak Galerkin Finite Element Methods for a Quasistatic Maxwell Viscoelastic Model
Year: 2023
Author: Zimo Zhu, Xiaoping Xie, Jihong Xiao, Zimo Zhu, Xiaoping Xie
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 1 : pp. 79–110
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2022-0024
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 1 : pp. 79–110
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Quasistatic Maxwell viscoelastic model weak Galerkin method semi-discrete scheme fully discrete scheme error estimate.