Finite element methods for second order linear hyperbolic interface problems

The aim of this paper is to study finite element methods and their convergence for hyperbolic interface problems. Both semidiscrete and fully discrete schemes are analyzed. Optimal a priori error estimates in the L2L2 and H1H1 norms are derived for a finite element discretization where interface triangles are assumed to be curved triangles instead of straight triangles. The interfaces and boundaries of the domains are assumed to be smooth for our purpose.