A posteriori error estimates by recovered gradients in parabolic finite element equations

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 elliptic theory can be extended to the parabolic problems provided the time-step error is smaller than the space-discretization error. Numerical illustrations confirming the theoretical results are given. Our results are not practical in the sense that various constants can not be estimated realistically. They are conceptual in nature. AMS subject classification (2000)  65M60, 65M20, 65M15