The effect of spatial quadrature on the semidiscrete finite element Galerkin method for a strongly damped wave equation

Abstract

The purpose of this article is to study the effect of spatial quadrature on the semidiscrete finite element Galerkin approximations to a linear strongly damped wave equation. Based on a nonstandard energy formulation, optimal order error estimates are derived for all time t > 0. More precisely, for the spatially discrete scheme, optimal order error estimates in L-2 and H-1 norms are proved for nonsmooth initial data. Further, quasi-optimal order error estimate is derived in L-infinity norm for nonsmooth initial data.