A polygonal discontinuous Galerkin method with minus one stabilization

Author:

Bertoluzza SilviaORCID,Prada DanieleORCID

Abstract

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.

Funder

European Research Council

Publisher

EDP Sciences

Subject

Applied Mathematics,Modeling and Simulation,Numerical Analysis,Analysis,Computational Mathematics

Reference33 articles.

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2. Multiscale Hybrid-Mixed Method

3. Discrete Interpolation Norms with Applications

4. The nonconforming virtual element method

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1. Algebraic representation of dual scalar products and stabilization of saddle point problems;Rendiconti Lincei - Matematica e Applicazioni;2022-02-21

2. A p-robust polygonal discontinuous Galerkin method with minus one stabilization;Mathematical Models and Methods in Applied Sciences;2021-10-29

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