A Posteriori Error Analysis for Semidiscrete Semilinear Parabolic Problems

Abstract

Optimal order a posteriori error bounds in $L_{\infty }(L_{2})$ norm are derived for semidiscrete semilinear parabolic problems using various assumptions on the forcing term. Standard continuous Galerkin (conforming) finite element method is employed. Our main tools in deriving these error estimates are the elliptic reconstruction technique, with the aid of Grönwall’s lemma and continuation argument.