Constructive error estimates for a full-discretized periodic solution of heat equation by spatial finite-element and time spectral method

Abstract

We consider the constructive a priori error estimates for a full discrete approximation of a periodic solution for the heat equation. Our numerical scheme is based on the finite element semidiscretization in space direction combined with the Fourier expansion in time. We derive the optimal order explicit H1 and L2 error estimates which play an important role in the numerical verification method of exact solutions for nonlinear parabolic equations. Several numerical examples which confirm the theoretical results will be presented.