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A High Order Explicit Time Finite Element Method for the Acoustic Wave Equation with Discontinuous Coefficients

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.

Author Details

Zhiming Chen

Yong Liu

Xueshuang Xiang