@Article{NMTMA-16-1,
author = {Zimo, Zhu and Xie, Xiaoping and Xiao, Jihong and Zimo, Zhu and Xie, Xiaoping},
title = {Semi-Discrete and Fully Discrete Weak Galerkin Finite Element Methods for a Quasistatic Maxwell Viscoelastic Model},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2023},
volume = {16},
number = {1},
pages = {79--110},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2022-0024},
url = {https://global-sci.com/article/90199/semi-discrete-and-fully-discrete-weak-galerkin-finite-element-methods-for-a-quasistatic-maxwell-viscoelastic-model}
}