On Maximum Norm Estimates for Ritz-Volterra Projection with Applications to Some Time Dependent Problems

Abstract

The stability in $L^\infty$-norm is considered for the Ritz-Volterra projection and some applications are presented in this paper. As a result, point-wise error estimates are established for the finite element approximation for the parabolic integro-differential equation, Sobolev equations, and a diffusion equation with non-local boundary value problem.