Volume 50, Number 3, May-June 2016
Special Issue – Polyhedral discretization for PDE
|Page(s)||699 - 725|
|Published online||23 May 2016|
hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes
Department of Mathematics, University of Leicester,
2 Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK & School of Applied Mathematical and Physical Sciences, National Technical University of Athens, 15780 Athens, Greece
3 School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK
Received: 14 April 2015
Revised: 10 August 2015
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.
Mathematics Subject Classification: 65N30 / 65N50 / 65N55
Key words: Discontinuous Galerkin; polygonal elements; polyhedral elements; hp-finite element methods; inverse estimates; 𝒫-basis; PDEs with nonnegative characteristic form
© EDP Sciences, SMAI 2016
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