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.
Highlights
1 Introduction In this paper, we investigate the space-time continuous finite element (STCFE) method for two-dimensional ( D) viscoelastic wave equation
4 Numerical experiments we provide two numerical examples to verify the efficiency and feasibility of the STCFE algorithm
From these tables we know that the second-order accuracy in the L and L (L ) norms and the first-order accuracy in the H and L (H ) norms with respect to space and the third-order accuracy in the L, H, L (L ), and L (H ) norms with respect to time are derived, which further verify the efficiency and feasibility of the STCFE method
Summary
We investigate the space-time continuous finite element (STCFE) method for two-dimensional ( D) viscoelastic wave equation. Though the researches of numerical solutions of viscoelastic wave equation have made a great progress (see, e.g., [ – ]), most of the existing papers either used the classical finite element (FE) methods or used finite difference (FD) schemes as discretization tools (see [ , ]). Our estimates are obtained without any restriction conditions between temporal and spatial grid sizes, so that our method is more suitable for practical applications and is different from the existing methods (see, e.g., [ – ]). It is a kind of improvement and development of the existing papers.
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