Ritz-Volterra Projections to Finite-Element Spaces and Applications to Integrodifferential and Related Equations

The object of this paper is to investigate the convergence of finite-element approximations to solutions of parabolic and hyperbolic integrodifferential equations, and also of equations of Sobolev and viscoelasticity type. The concept of Ritz-Volterra projection will be seen to unify much of the analysis for the different types of problems. Optimal order error estimates are obtained in Lpfor$2 \leqq p < \infty$, and almost optimal order pointwise results given.