A note on devising HDG+ projections on polyhedral elements
Numerical Analysis
2020-06-23 v2 Numerical Analysis
Abstract
In this note, we propose a simple way of constructing HDG+ projections on polyhedral elements. The projections enable us to analyze the Lehrenfeld-Sch\"{o}berl HDG (HDG+) methods in a very concise manner, and make many existing analysis techniques of standard HDG methods reusable for HDG+. The novelty here is an alternative way of constructing the projections without using -decompositions as a middle step. This extends our previous results [S. Du and F.-J. Sayas, SpringerBriefs in Mathematics (2019)] (elliptic problems) and [S. Du and F.-J. Sayas, Math.~Comp.~89~(2020), 1745-1782] (elasticity) to polyhedral meshes.
Keywords
Cite
@article{arxiv.2002.07879,
title = {A note on devising HDG+ projections on polyhedral elements},
author = {Shukai Du and Francisco-Javier Sayas},
journal= {arXiv preprint arXiv:2002.07879},
year = {2020}
}