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 - <p style="text-align: justify;">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.</p>