Convergence of finite element method for linear second-order wave equations with discontinuous coefficients

摘要

A finite element method is proposed and analyzed for hyperbolic problems with discontinuous coefficients. The main emphasize is given on the convergence of such method. Due to low global regularity of the solutions, the error analysis of the standard finite element method is difficult to adopt for such problems. For a practical finite element discretization, optimal error estimates in L~∞(L~2) and L~∞(H~1) norms are established for continuous time discretization. Further, a fully discrete scheme based on a symmetric difference approximation is considered, and optimal order convergence in L~∞(H~1) norm is established.