The DPG Method for the Convection-Reaction Problem Revisited

Technical Report · 01 March 2021

DOI:https://doi.org/10.2172/1772894· OSTI ID:1772894

Demkowicz, Leszek ^[1]; Roberts, Nathan V. ^[2]

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1. Univ. of Texas, Austin, TX (United States)
2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

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 the direct construction of a global Fortin operator; 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

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Univ. of Texas, Austin, TX (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• DOE Contract Number: AC04-94AL85000; NA0003525
• OSTI ID: 1772894
• Report Number(s): SAND--2021-3435R; 694968
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
97 MATHEMATICS AND COMPUTING