| Issue |
ESAIM: M2AN
Volume 58, Number 3, May-June 2024
|
|
|---|---|---|
| Page(s) | 1087 - 1106 | |
| DOI | https://doi.org/10.1051/m2an/2024019 | |
| Published online | 26 June 2024 | |
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
Inria Univ. Lille and Laboratoire Paul Painlevé, 59655 Villeneuve-d’Ascq, France
* Corresponding author: theophile.chaumont@inria.fr
Received:
30
August
2022
Accepted:
13
March
2024
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.
Mathematics Subject Classification: 35J05 / 65N12 / 65N15 / 65N30
Key words: a priori / error estimates / a posteriori error estimates / Aubin–Nitsche trick / discontinuous Galerkin / Helmholtz problems / interior penalty / minimal regularity
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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