A priori L∞(L2) error estimates for finite element approximations to the wave equation with interface

In this article a fitted finite element method is proposed and analyzed for wave equation with discontinuous coefficients. Typical semidiscrete and an implicit fully discrete schemes are presented and analyzed. Optimal a priori error estimates for both semidiscrete and fully discrete schemes are proved in L∞(L2) norm. The convergence analysis relies heavily on time reconstructions of continuous and discrete solutions, in conjunction with some known results on elliptic interface problems. Finally, a numerical experiment is presented to verify our theoretical result.