The DPG Method for the Convection-Reaction Problem, Revisited

Demkowicz, Leszek Feliks; Roberts, Nathan V.; Muñoz-Matute, Judit

doi:10.1515/cmam-2021-0149

The DPG Method for the Convection-Reaction Problem, Revisited

Journal Article · 22 June 2022 · Computational Methods in Applied Mathematics

DOI:https://doi.org/10.1515/cmam-2021-0149· OSTI ID:1883191

^[1]; Roberts, Nathan V. ^[2]; Muñoz-Matute, Judit ^[3]

Univ. of Texas, Austin, TX (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Univ. of Texas, Austin, TX (United States); Basque Center for Applied Mathematics, Bilbao (Spain)

In this work, 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.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program; National Science Foundation (NSF); European Research Council (ERC)

Grant/Contract Number:: NA0003525

OSTI ID:: 1883191

Report Number(s):: SAND2022-7111J; 706744

Journal Information:: Computational Methods in Applied Mathematics, Journal Name: Computational Methods in Applied Mathematics Journal Issue: 1 Vol. 23; ISSN 1609-4840

Publisher:: de GruyterCopyright Statement

Country of Publication:: United States

Language:: English

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