Logarithm cannot be removed in maximum norm error estimates for linear finite elements in 3D
Numerical Analysis
2018-10-24 v3
Abstract
For linear finite element discretizations of the Laplace equation in three dimensions, we give an example of a tetrahedral mesh in the cubic domain for which the logarithmic factor cannot be removed from the standard upper bounds on the error in the maximum norm.
Cite
@article{arxiv.1710.03262,
title = {Logarithm cannot be removed in maximum norm error estimates for linear finite elements in 3D},
author = {Natalia Kopteva},
journal= {arXiv preprint arXiv:1710.03262},
year = {2018}
}