Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

A note on devising HDG+ projections on polyhedral elements


Authors: Shukai Du and Francisco-Javier Sayas
Journal: Math. Comp. 90 (2021), 65-79
MSC (2010): Primary 65N30, 65N15
DOI: https://doi.org/10.1090/mcom/3573
Published electronically: September 23, 2020
MathSciNet review: 4166453
Full-text PDF
View in AMS MathViewer New

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 65N30, 65N15

Retrieve articles in all journals with MSC (2010): 65N30, 65N15


Additional Information

Shukai Du
Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
MR Author ID: 1303285
Email: shukaidu@udel.edu

Francisco-Javier Sayas
Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
MR Author ID: 621885

DOI: https://doi.org/10.1090/mcom/3573
Keywords: Discontinuous Galerkin, hybridization, polyhedral meshes, superconvergence, elasticity
Received by editor(s): October 7, 2019
Received by editor(s) in revised form: May 29, 2020
Published electronically: September 23, 2020
Additional Notes: This work was partially supported by the NSF grant DMS-1818867.
Article copyright: © Copyright 2020 American Mathematical Society