| Issue |
ESAIM: M2AN
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
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|---|---|---|
| Page(s) | S785 - S810 | |
| DOI | https://doi.org/10.1051/m2an/2020059 | |
| Published online | 26 February 2021 | |
A polygonal discontinuous Galerkin method with minus one stabilization
IMATI “E. Magenes”, CNR, Pavia, Italy
* Corresponding author: silvia.bertoluzza@imati.cnr.it
Received:
26
September
2019
Accepted:
12
August
2020
We propose a discontinuous Galerkin method for the Poisson equation on polygonal tessellations in two dimensions, stabilized by penalizing, locally in each element K, a residual term involving the fluxes, measured in the norm of the dual of H1 (K). The scalar product corresponding to such a norm is numerically realized via the introduction of a (minimal) auxiliary space inspired by the Virtual Element Method. Stability and optimal error estimates in the broken H1 norm are proven under a weak shape regularity assumption allowing the presence of very small edges. The results of numerical tests confirm the theoretical estimates.
Key words: Discontinuous Galerkin method / polygonal tessellation / minus one stabilization
Key words:
© EDP Sciences, SMAI 2021
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