On the efficiency of a posteriori error estimators for parabolic partial differential equations in the energy norm
Abstract
For the model problem of the heat equation discretized by an implicit Euler method in time and a conforming finite element method in space, we prove the efficiency of a posteriori error estimators with respect to the energy norm of the error, when considering the numerical solution as the average between the usual continuous piecewise affine-in-time and piecewise constant-in-time reconstructions. This illustrates how the efficiency of the estimators is not only possibly dependent on the choice of norm, but also on the choice of notion of numerical solution.
Fields of Study & Subjects
Numerical methods in inverse problems
Publication details
- Journal / source
- SMAI Journal of Computational Mathematics
- Volume
- 12
- Pages
- 27–42
- Publication date
- 2 March 2026
- Language
- EN