Product Gauss quadrature rules vs. cubature rules in the meshless local Petrov-Galerkin method

Authors:
Annamaria Mazzia;Giorgio Pini
Affiliations:
Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Universití degli Studi di Padova, via Trieste 63 - 35121 Padova, Italy;Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Universití degli Studi di Padova, via Trieste 63 - 35121 Padova, Italy
Venue:
Journal of Complexity
Year:
2010

Citing 5
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Abstract

A crucial point in the implementation of meshless methods such as the meshless local Petrov-Galerkin (MLPG) method is the evaluation of the domain integrals arising over circles in the discrete local weak form of the governing partial differential equation. In this paper we make a comparison between the product Gauss numerical quadrature rules, which are very popular in the MLPG literature, with cubature formulas specifically constructed for the approximation of an integral over the unit disk, but not yet applied in the MLPG method, namely the spherical, the circularly symmetrical and the symmetric cubature formulas. The same accuracy obtained with 64x64 points in the product Gauss rules may be obtained with symmetric quadrature formulas with very few points.