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In this paper, we propose a novel high order unfitted finite element methodon Cartesian meshes for solving the acoustic wave equation with discontinuouscoefficients having complex interface geometry. The unfitted finite elementmethod does not require any penalty to achieve optimal convergence. We alsointroduce a new explicit time discretization method for the ODE systemresulting from the spatial discretization of the wave equation. The strongstability and optimal $hp$-version error estimates both in time and space areestablished. Numerical examples confirm our theoretical results.

A high order explicit time finite element method for the acoustic wave equation with discontinuous coefficients