Approximation of linear hyperbolic interface problems on finite element: Some new estimates

Abstract

Finite element solution of a linear hyperbolic interface problem with time discretization based on 3-step implicit scheme is proposed. Quasi-uniform triangular elements are used for the spatial discretization. With low regularity assumption on the solution across the interface, the stability of the scheme is established and almost optimal convergence rates in L2(Ω) and H1(Ω) norms are obtained. In terms of matrices arising in the scheme, we show that the discrete solution satisfies the maximum principle under certain conditions on the mesh parameter h and time step k. Numerical experiments are presented to support the theoretical results.