Sharp $L^\infty$ estimates of HDG methods for Poisson equation II: 3D
Numerical Analysis
2021-10-18 v1 Numerical Analysis
Abstract
In [SIAM J. Numer. Anal., 59 (2), 720-745], we proved quasi-optimal estimates (up to logarithmic factors) for the solution of Poisson's equation by a hybridizable discontinuous Galerkin (HDG) method. However, the estimates only work in 2D. In this paper, we obtain sharp (without logarithmic factors) estimates for the HDG method in both 2D and 3D. Numerical experiments are presented to confirm our theoretical result.
Cite
@article{arxiv.2110.07795,
title = {Sharp $L^\infty$ estimates of HDG methods for Poisson equation II: 3D},
author = {Gang Chen and Peter Monk and Yangwen Zhang},
journal= {arXiv preprint arXiv:2110.07795},
year = {2021}
}