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

In this paper, we propose a novel high order explicit time discretization method for the acoustic wave equation with discontinuous coefficients. The space discretization is based on the unfitted finite element method in the discontinuous Galerkin framework which allows us to treat problems with complex interface geometry on Cartesian meshes. The strong stability and optimal $hp$-version error estimates both in time and space are established. Numerical examples confirm our theoretical results.