English

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.

Keywords

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}
}