The DPG Method for the Convection-Reaction Problem, Revisited

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...

ver descrição completa

Detalhes bibliográficos
Autores: Demkowicz, L., Roberts, N.V., Muñoz-Matute, J.
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2022
País:España
Recursos:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1512
Acesso em linha:http://hdl.handle.net/20.500.11824/1512
Access Level:acceso abierto
Palavra-chave:Convection-Reaction
Discontinuous Petrov-Galerkin
Descrição
Resumo: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.