The finite element method for parabolic equations. I. A posteriori error estimation (Q790597)

Computable a posteriori estimates of the spatial discretization error in the finite element method of lines solution of parabolic equations are analyzed for time-independent space meshes. Theoretical results are given specifying sufficient conditions on the regularity of the solution and on the mesh which guarantees the effectiveness of the error estimator. Numerical examples are given which indicate that the estimates are more effective than the theory would suggest.