APPROXIMATE SOLUTION OF NONLINEAR HYPERBOLIC EQUATIONS WITH HOMOGENEOUS JUMP CONDITIONS

Abstract

We present the error analysis of a class of second-order nonlinear hyperbolic interface problems where the spatial and time discretizations are based on a finite element method and linearized backward difference scheme respectively. Both semi-discrete and fully discrete schemes are analyzed with the assumption that the interface is arbitrary but smooth. Almost optimal convergence rate in the H1-norm is obtained. Numerical examples are given to support the theoretical result.