Volume 5, Issue 4
A High Order Explicit Time Finite Element Method for the Acoustic Wave Equation with Discontinuous Coefficients

Zhiming Chen, Yong Liu & Xueshuang Xiang

CSIAM Trans. Appl. Math., 5 (2024), pp. 735-787.

Published online: 2024-11

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  • 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.

  • AMS Subject Headings

65M12, 65M60

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COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-5-735, author = {Chen , ZhimingLiu , Yong and Xiang , Xueshuang}, title = {A High Order Explicit Time Finite Element Method for the Acoustic Wave Equation with Discontinuous Coefficients}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2024}, volume = {5}, number = {4}, pages = {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.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.SO-2023-0043}, url = {http://global-sci.org/intro/article_detail/csiam-am/23586.html} }
TY - JOUR T1 - A High Order Explicit Time Finite Element Method for the Acoustic Wave Equation with Discontinuous Coefficients AU - Chen , Zhiming AU - Liu , Yong AU - Xiang , Xueshuang JO - CSIAM Transactions on Applied Mathematics VL - 4 SP - 735 EP - 787 PY - 2024 DA - 2024/11 SN - 5 DO - http://doi.org/10.4208/csiam-am.SO-2023-0043 UR - https://global-sci.org/intro/article_detail/csiam-am/23586.html KW - Explicit time discretization, strong stability, unfitted finite element, $hp$ error estimates. AB -

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.

Chen , ZhimingLiu , Yong and Xiang , Xueshuang. (2024). A High Order Explicit Time Finite Element Method for the Acoustic Wave Equation with Discontinuous Coefficients. CSIAM Transactions on Applied Mathematics. 5 (4). 735-787. doi:10.4208/csiam-am.SO-2023-0043
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