Aubin--Nitsche-type estimates for space-time FOSLS for parabolic PDEs
Numerical Analysis
2025-04-30 v1 Numerical Analysis
Abstract
We develop Aubin--Nitsche-type estimates for recently proposed first-order system least-squares finite element methods (FOSLS) for the heat equation. Under certain assumptions, which are satisfied if the spatial domain is convex and the heat source and initial datum are sufficiently smooth, we prove that the error of approximations of the scalar field variable converges at a higher rate than the overall error. Furthermore, a higher-order conservation property is shown. In addition, we discuss quasi-optimality in weaker norms. Numerical experiments confirm our theoretical findings.
Keywords
Cite
@article{arxiv.2412.04651,
title = {Aubin--Nitsche-type estimates for space-time FOSLS for parabolic PDEs},
author = {Thomas Führer and Gregor Gantner},
journal= {arXiv preprint arXiv:2412.04651},
year = {2025}
}