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arXiv · 2202.09951

Semi-discrete and fully discrete weak Galerkin finite element methods for a quasistatic Maxwell viscoelastic model

Jihong Xiao·Zimo Zhu·Xiaoping Xie
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Abstract

This paper considers weak Galerkin finite element approximations for a quasistatic Maxwell viscoelastic model. The spatial discretization uses piecewise polynomials of degree $k \ (k\geq 1)$ 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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Jihong Xiao, Zimo Zhu, Xiaoping Xie. 2022-02-21. Semi-discrete and fully discrete weak Galerkin finite element methods for a quasistatic Maxwell viscoelastic model. https://arxiv.org/abs/2202.09951

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