A High Order Explicit Time Finite Element Method for the Acoustic Wave Equation with Discontinuous Coefficients (CSIAM Transactions on Applied Mathematics, 2024)
In this paper, we propose a novel high order unfitted finite element methodon Cartesian meshes for solving the acoustic wave equation with discontinuous coefficients having complex interface geometry. The unfitted finite element method doesnot require any penalty to achieve optimal convergence. We also introduce a new explicit time discretization method for the ordinary differential equation (ODE) systemresulting from the spatial discretization of the wave equation. The strong stability andoptimal $hp$-version error estimates both in time and space are established. Numericalexamples confirm our theoretical results.