TY - JOUR
T1 - Semi-Discrete and Fully Discrete Weak Galerkin Finite Element Methods for a Quasistatic Maxwell Viscoelastic Model
AU - Xiao , Jihong
AU - Zhu , Zimo
AU - Xie , Xiaoping
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 79
EP - 110
PY - 2023
DA - 2023/01
SN - 16
DO - http://doi.org/10.4208/nmtma.OA-2022-0024
UR - https://global-sci.org/intro/article_detail/nmtma/21344.html
KW - Quasistatic Maxwell viscoelastic model, weak Galerkin method, semi-discrete scheme, fully discrete scheme, error estimate.
AB - <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>