A posteriori error estimates for finite element discretizations of the heat equation. (English) Zbl 1168.65418

Verfürth, R.

Calcolo 40, No. 3, 195-212 (2003).

Summary: We consider discretizations of the heat equation by \(A\)-stable \(\theta\)-schemes in time and conforming finite elements in space. For these discretizations we derive residual a posteriori error indicators. The indicators yield upper bounds on the error which are global in space and time and yield lower bounds that are global in space and local in time. The ratio between upper and lower bounds is uniformly bounded in time and does not depend on any step-size in space or time. Moreover, there is no restriction on the relation between the step-sizes in space and time.

MSC:

65N30

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs