A High Order Explicit Time Finite Element Method for the Acoustic Wave Equation with Discontinuous Coefficients
Year: 2024
Author: Zhiming Chen, Yong Liu, Xueshuang Xiang
CSIAM Transactions on Applied Mathematics, Vol. 5 (2024), Iss. 4 : pp. 735–787
Abstract
In this paper, we propose a novel high order unfitted finite element method on Cartesian meshes for solving the acoustic wave equation with discontinuous coefficients having complex interface geometry. The unfitted finite element method does not require any penalty to achieve optimal convergence. We also introduce a new explicit time discretization method for the ordinary differential equation (ODE) system resulting from the spatial discretization of the wave equation. The strong stability and optimal $hp$-version error estimates both in time and space are established. Numerical examples confirm our theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2023-0043
CSIAM Transactions on Applied Mathematics, Vol. 5 (2024), Iss. 4 : pp. 735–787
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 53
Keywords: Explicit time discretization strong stability unfitted finite element $hp$ error estimates.