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Fast Numerical Integration on Polytopic Meshes with Applications to Discontinuous Galerkin Finite Element Methods

Antonietti, Paola; Houston, Paul; Pennesi, Giorgio

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Authors

Paola Antonietti

PAUL HOUSTON PAUL.HOUSTON@NOTTINGHAM.AC.UK
Professor of Computational and Applied Maths

Giorgio Pennesi



Abstract

In this paper we present efficient quadrature rules for the numerical approximation of integrals of polynomial functions over general polygonal/polyhedral elements that do not require an explicit construction of a sub-tessellation into triangular/tetrahedral elements. The method is based on successive application of Stokes' theorem; thereby, the underlying integral may be evaluated using only the values of the integrand at the vertices of the polytopic domain, and hence leads to an exact cubature rule whose quadrature points are the vertices of the polytope. We demonstrate the capabilities of the proposed approach by efficiently computing the stiffness and mass matrices arising from hp-version symmetric interior penalty discontinuous Galerkin discretizations of second-order elliptic partial differential equations.

Citation

Antonietti, P., Houston, P., & Pennesi, G. (2018). Fast Numerical Integration on Polytopic Meshes with Applications to Discontinuous Galerkin Finite Element Methods. Journal of Scientific Computing, 77(3), 1339-1370. https://doi.org/10.1007/s10915-018-0802-y

Journal Article Type Article
Acceptance Date Jul 31, 2018
Online Publication Date Aug 29, 2018
Publication Date 2018-12
Deposit Date Aug 14, 2018
Publicly Available Date Sep 11, 2018
Journal Journal of Scientific Computing
Print ISSN 0885-7474
Electronic ISSN 1573-7691
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 77
Issue 3
Pages 1339-1370
DOI https://doi.org/10.1007/s10915-018-0802-y
Public URL https://nottingham-repository.worktribe.com/output/1031787
Publisher URL https://www.springerprofessional.de/en/fast-numerical-integration-on-polytopic-meshes-with-applications/16084184?fulltextView=true
Contract Date Sep 11, 2018

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