Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 77, Issue 3, Pages 1339-1370Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-018-0802-y
Keywords
Numerical integration; Polygonal/polyhedral meshes; hp-discontinuous Galerkin method
Categories
Funding
- SIR Project - MIUR - Italian Ministry of Education, Universities and Research [RBSI14VT0S]
- Fondazione Cariplo and Regione Lombardia [2015-0182]
- GNCS-INdAM
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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 and its derivatives 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.
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