Work

On the efficiency of a posteriori error estimators for parabolic partial differential equations in the energy norm

Year: 2026

Type: article

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.

Source: SMAI Journal of Computational Mathematics

DOI: 10.5802/jcm.142

Author: Iain Smears

Institution: University College London

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

Funder: Engineering and Physical Sciences Research Council

OpenAlex ID: W4415310464