On Generalized Gaussian Quadrature

Generalized Gaussian Quadrature Rules in Enriched Finite Element Methods

In this paper, we present new Gaussian integration schemes for the efficient and accurate evaluation of weak form integrals that arise in enriched finite element methods. For discontinuous functions we present an algorithm for the construction of Gauss-like quadrature rules over arbitrarily-shaped elements without partitioning. In case of singular integrands, we introduce a new polar transforma...

Anti-Gaussian quadrature formulas

An anti-Gaussian quadrature formula is an (n+ 1)-point formula of degree 2n− 1 which integrates polynomials of degree up to 2n+ 1 with an error equal in magnitude but of opposite sign to that of the n-point Gaussian formula. Its intended application is to estimate the error incurred in Gaussian integration by halving the difference between the results obtained from the two formulas. We show tha...

The Gaussian Quadrature Method

Product Gaussian quadrature on circular lunes

Resorting to recent results on subperiodic trigonometric quadrature, we provide three product Gaussian quadrature formulas exact on algebraic polynomials of degree n on circular lunes. The first works on any lune, and has n+O(n) cardinality. The other two have restrictions on the lune angular intervals, but their cardinality is n/2 +O(n). 2000 AMS subject classification: 65D32.

On the Universalityof the Gaussian Quadrature FormulaKnut

Several deenitions of universality of an n-point quadrature formula Q n are discussed. Universality means that Q n is able to compete with the respective optimal formula in many classes of functions. It is proved in a certain sense that the Gaus-sian quadrature formula satisses such a universality criterion. The underlying classes of functions are In each of these classes, we loose at most the ...