Supplement to the Convergence of Galerkin Approximation Schemes for Second-Order Hyperbolic Equations With Dissipation

Abstract

In this paper we consider certain semidiscrete and fully discrete Galerkin approximations to the solution of an initial-boundary value problem for a second-order hyperbolic equation with a dissipative term. Estimates are obtained in the energy and negative norms associated with the problem, yielding in particular //'-and L2-error estimates. The approximation to the initial data is taken, in this case, as the projection with respect to the energy inner product, onto the approximating space. We also obtain estimates for higher-order time derivatives.