A unified approach to maximum-norm a posteriori error estimation for second-order time discretisations of parabolic equations
Numerical Analysis
2023-04-05 v1 Numerical Analysis
Abstract
A class of linear parabolic equations are considered. We derive a common framework for the a posteriori error analysis of certain second-order time discretisations combined with finite element discretisations in space. In particular we study the Crank-Nicolson method, the extrapolated Euler method, the backward differentiation formula of order 2 (BDF-2), the Lobatto IIIC method and a two-stage SDIRK method. We use the idea of elliptic reconstructions and certain bounds for the Green's function of the parabolic operator.
Keywords
Cite
@article{arxiv.2304.01637,
title = {A unified approach to maximum-norm a posteriori error estimation for second-order time discretisations of parabolic equations},
author = {Torsten Linß and Martin Ossadnik and Goran Radojev},
journal= {arXiv preprint arXiv:2304.01637},
year = {2023}
}
Comments
12 pages. arXiv admin note: substantial text overlap with arXiv:2208.08153