Duality analysis of interior penalty discontinuous Galerkin methods under minimal regularity and application to the a priori and a posteriori error analysis of Helmholtz problems
| Autor: | Chaumont-Frelet, T. |
|---|---|
| Přispěvatelé: | Modélisation et méthodes numériques pour le calcul d'interactions onde-matière nanostructurée (ATLANTIS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Laboratoire Jean Alexandre Dieudonné (LJAD) |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
a posteriori error estimates
a priori error estimates Helmholtz problems Numerical Analysis (math.NA) interior penalty minimal regularity Mathematics - Analysis of PDEs FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Aubin-Nitsche trick Mathematics - Numerical Analysis [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Analysis of PDEs (math.AP) discontinuous Galerkin |
| Popis: | We consider interior penalty discontinuous Galerkin discretizations of time-harmonic wave propagation problems modeled by the Helmholtz equation, and derive novel a priori and a posteriori estimates. Our analysis classically relies on duality arguments of Aubin-Nitsche type, and its originality is that it applies under minimal regularity assumptions. The estimates we obtain directly generalize known results for conforming discretizations, namely that the discrete solution is optimal in a suitable energy norm and that the error can be explicitly controlled by a posteriori estimators, provided the mesh is sufficiently fine. |
| Databáze: | OpenAIRE |
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