Publication Results

Code: 03/2018
Title: Fast numerical integration on polytopic meshes with applications to discontinuous Galerkin finite element methods
Date: Saturday 13th January 2018
Author(s) : Antonietti, P. F.; Houston, P.; Pennesi, G.
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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.

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Journal of Scientific Computing - Springer