A space-time continuous finite element method for 2D viscoelastic wave equation

Abstract

In this article, we establish a space-time continuous finite element (STCFE) method for viscoelastic wave equation. The existence, uniqueness, and stability of the STCFE solutions are proved, and the optimal rates of convergence of STCFE solutions are obtained without any time and space mesh size restrictions. Two numerical examples on unstructured meshes are employed to verify the efficiency and feasibility of the STCFE method and to check the correctness of theoretical conclusions.