A Polygonal Discontinuous Galerkin Method with Minus One Stabilization

Silvia Bertoluzza; Daniele Prada

doi:10.1051/m2an/2020059

A Polygonal Discontinuous Galerkin Method with Minus One Stabilization

Numerical Analysis 2021-03-11 v3 Numerical Analysis

Authors: Silvia Bertoluzza , Daniele Prada

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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 $H^1(K)$ . 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 $H^1$ 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.

Keywords

discontinuous galerkin method discontinuous galerkin methods galerkin methods

Cite

@article{arxiv.1805.04196,
  title  = {A Polygonal Discontinuous Galerkin Method with Minus One Stabilization},
  author = {Silvia Bertoluzza and Daniele Prada},
  journal= {arXiv preprint arXiv:1805.04196},
  year   = {2021}
}

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23 pages

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