An introduction to the a posteriori error analysis of parabolic partial differential equations
Numerical Analysis
2025-12-02 v1 Numerical Analysis
Abstract
This article provides a brief introduction to the a posteriori error analysis of parabolic partial differential equations, with an emphasis on challenges distinct from those of steady-state problems. Using the heat equation as a model problem, we examine the crucial influence of the choice of error norm, as well as the choice of notion of reconstruction of the discrete solution, on the analytical properties of the resulting estimators, especially in terms of the efficiency of the estimators.
Cite
@article{arxiv.2511.00245,
title = {An introduction to the a posteriori error analysis of parabolic partial differential equations},
author = {Iain Smears},
journal= {arXiv preprint arXiv:2511.00245},
year = {2025}
}