A note on devising HDG+ projections on polyhedral elements

Du, Shukai; Sayas, Francisco-Javier

doi:10.1090/mcom/3573

A note on devising HDG+ projections on polyhedral elements
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by Shukai Du and Francisco-Javier Sayas HTML | PDF

Math. Comp. 90 (2021), 65-79 Request permission

Abstract:

In this paper, we propose a simple way of constructing HDG+ projections on polyhedral elements. The projections enable us to analyze the Lehrenfeld–Schöberl 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 $M$-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), pp. 1745–1782] (elasticity) to polyhedral meshes.

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