hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes
journal contributionposted on 2016-08-30, 15:11 authored by Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis, Paul Houston
We consider the hp-version interior penalty discontinuous Galerkin finite element method (DGFEM) for the numerical approximation of the advection-diffusion-reaction equation on general computational meshes consisting of polygonal/polyhedral (polytopic) elements. In particular, new hp-version a priori error bounds are derived based on a specific choice of the interior penalty parameter which allows for edge/face-degeneration. The proposed method employs elemental polynomial bases of total degree p (𝒫p-basis) defined in the physical coordinate system, without requiring the mapping from a given reference or canonical frame. Numerical experiments highlighting the performance of the proposed DGFEM are presented. In particular, we study the competitiveness of the p-version DGFEM employing a 𝒫p-basis on both polytopic and tensor-product elements with a (standard) DGFEM employing a (mapped) 𝒬p-basis. Moreover, a computational example is also presented which demonstrates the performance of the proposed hp-version DGFEM on general agglomerated meshes.
CitationESAIM: Mathematical Modelling and Numerical Analysis, 2016, 50 (3), pp. 699-725
Author affiliation/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics
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