Stabilized cut discontinuous galerkin methods for advection-reaction problems
| Autor: | Simon Sticko, Ceren Gürkan, André Massing |
|---|---|
| Přispěvatelé: | Gürkan, Ceren |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Advection
Applied Mathematics Mathematical analysis Domain (mathematical analysis) Stabilization Mathematics::Numerical Analysis Computational Mathematics A priori error estimates Discontinuous Galerkin method Advection-reaction problems Discontinuous Galerkin Condition number Cut finite element method Mathematics |
| Popis: | We develop novel stabilized cut discontinuous Galerkin methods for advection-reaction problems. The domain of interest is embedded into a structured, unfitted background mesh in \BbbR d where the domain boundary can cut through the mesh in an arbitrary fashion. To cope with robustness problems caused by small cut elements, we introduce ghost penalties in the vicinity of the embedded boundary to stabilize certain (semi-)norms associated with the advection and reaction operator. A few abstract assumptions on the ghost penalties are identified enabling us to derive geometrically robust and optimal a priori error and condition number estimates for the stationary advection-reaction problem which hold irrespective of the particular cut configuration. Possible realizations of suitable ghost penalties are discussed. The theoretical results are corroborated by a number of computational studies for various approximation orders and for two- and three-dimensional test problems. Kempe Foundation Swedish Research Council |
| Databáze: | OpenAIRE |
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