A Posteriori Error Estimates by Recovered Gradients in Parabolic Finite Element Equations

Abstract

This paper considers a posteriori error estimates by averaged gradients in second order parabolic problems. Fully discrete schemes are treated. The theory from the elliptic case as to when such estimates are asymptotically exact, on an element, is carried over to the error on an element at a given time. The basic principle is that the time-step error needs to be smaller than the space-discretization error. Numerical illustrations are given