English

Error estimates for completely discrete FEM in energy-type and weaker norms

Numerical Analysis 2026-02-04 v3 Numerical Analysis

Abstract

The paper presents error estimates within a unified abstract framework for the analysis of FEM for boundary value problems with linear diffusion-convection-reaction equations and boundary conditions of mixed type. Since neither conformity nor consistency properties are assumed, the method is called completely discrete. We investigate two different stabilized discretizations and obtain stability and optimal error estimates in energy-type norms and, by generalizing the Aubin-Nitsche technique, optimal error estimates in weaker norms.

Keywords

Cite

@article{arxiv.2301.06860,
  title  = {Error estimates for completely discrete FEM in energy-type and weaker norms},
  author = {Lutz Angermann and Peter Knabner and Andreas Rupp},
  journal= {arXiv preprint arXiv:2301.06860},
  year   = {2026}
}