The DPG Method for the Convection-Reaction Problem, Revisited-Reference-Cited by-同舟云学术

The DPG Method for the Convection-Reaction Problem, Revisited

Published:2022-06-22 Issue:1 Volume:23 Page:93-125
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Demkowicz Leszek Feliks¹^ORCID,Roberts Nathan V.²,Muñoz-Matute Judit³

Affiliation:

1. Oden Institute , The University of Texas , Austin , USA

2. Center for Computer Research , Sandia National Laboratories , Albuquerque , USA

3. Oden Institute , The University of Texas , Austin , USA ; and Basque Center for Applied Mathematics, Bilbo, Spain

Abstract

Abstract We study both conforming and non-conforming versions of the practical DPG method for the convection-reaction problem. We determine that the most common approach for DPG stability analysis – construction of a local Fortin operator – is infeasible for the convection-reaction problem. We then develop a line of argument based on a direct proof of discrete stability; we find that employing a polynomial enrichment for the test space does not suffice for this purpose, motivating the introduction of a (two-element) subgrid mesh. The argument combines mathematical analysis with numerical experiments.

Funder

Sandia National Laboratories

National Science Foundation

H2020 Marie Skłodowska-Curie Actions

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/cmam-2021-0149/pdf

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