A Posteriori Error Analysis for Semidiscrete Semilinear Parabolic Problems

摘要

Optimal order a posteriori error bounds in L_∞ (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 Gronwall's lemma and continuation argument.