Constructive error estimates for full discrete approximation of periodic solution for heat equation

Abstract

We consider the constructive a priori error estimates for a full discrete numerical solution of the heat equation with time-periodic condition. Our numerical scheme is based on the finite element semidiscretization in space direction combined with an interpolation in time using the fundamental matrix for the semidiscretized problem. We derive the optimal order H1 and L2 error estimates that are critical in the numerical verification method of exact solutions for nonlinear parabolic equations. Several numerical examples that confirm the optimal rate of convergence are presented.