Finite volume element method for second order hyperbolic equations

Abstract

We discuss a priori error estimates for a semidiscrete piecewise linear finite volume element (FVE) approximation to a second order wave equationin a two-dimensional convex polygonal domain. Since the domain is convexpolygonal, a special attention has been paid to the limited regularity of theexact solution. Optimal error estimates in L², H¹ norms and quasioptimal estimates in L^∞ norm are discussed without quadrature and also with numericalquadrature. Numerical results confirm the theoretical order of convergence.