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DOE OSTI · 1883191

The DPG Method for the Convection-Reaction Problem, Revisited

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

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.

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97 MATHEMATICS AND COMPUTINGConvection-ReactionDiscontinuous Petrov–Galerkin

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Demkowicz, Leszek Feliks, Roberts, Nathan V., Muñoz-Matute, Judit. 2022-06-22. The DPG Method for the Convection-Reaction Problem, Revisited. https://doi.org/10.1515/cmam-2021-0149

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