Weak Galerkin finite element method for viscoelastic wave equations

Abstract In this article, we consider a weak Galerkin finite element method (WG-FEM) for solving one type of viscoelastic wave equation. A discrete weak gradient operator on discontinuous piecewise polynomials is used in the numerical scheme. We introduce both the semi- and fully-discrete WG-FEMs and establish the corresponding stability estimates. Optimal order error estimate in H 1 -norm is derived. Numerical experiments are preformed to verify the theoretical results.

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