Volume 55, 2021Regular 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
|Page(s)||S785 - S810|
|Published online||26 February 2021|
A polygonal discontinuous Galerkin method with minus one stabilization
IMATI “E. Magenes”, CNR, Pavia, Italy
* Corresponding author: firstname.lastname@example.org
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
© EDP Sciences, SMAI 2021
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