Please use this identifier to cite or link to this item:
Title: hp-Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes
Authors: Cangiani, Andrea
Dong, Zhaonan
Georgoulis, Emmanuil H.
Houston, Paul
First Published: 23-May-2016
Publisher: EDP Sciences / SMAI
Citation: ESAIM: Mathematical Modelling and Numerical Analysis, 2016, 50 (3), pp. 699-725
Abstract: 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.
DOI Link: 10.1051/m2an/2015059
ISSN: 0764-583X
eISSN: 1290-3841
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © EDP Sciences, SMAI 2016. Deposited with reference to the publisher’s archiving policy available on the SHERPA/RoMEO website.
Appears in Collections:Published Articles, Dept. of Mathematics

Files in This Item:
File Description SizeFormat 
Cangiani-Dong-Georgoulis-Houston_M2AN_2016.pdfPublished (publisher PDF)1.15 MBAdobe PDFView/Open

Items in LRA are protected by copyright, with all rights reserved, unless otherwise indicated.