Constructive A Priori Error Estimates for a Full Discrete Approximation of the Heat Equation

Abstract

In this paper, we consider the constructive a priori error estimates for a full discrete numerical solution of the heat equation. Our method is based on the finite element Galerkin method with an interpolation in time that uses the fundamental solution for semidiscretization in space. The present estimates play an essential role in the numerical verification method of exact solutions for the nonlinear parabolic equations. This implies that by utilizing the present results we could get the guaranteed a posteriori error estimates for various kinds of nonlinear evolutional problems. Our results can also be considered as an explicit optimal estimate with the limited regularity of solutions, which should be unknown up to the present.