Fictitious domain methods enable to solve physical problems on unfitted grids, thereby avoiding time-consuming and error prone meshing phases. However, an accurate integration of the weak formulation is still mandatory, leading need for efficient quadrature strategies in elements that are partially located domain. Various methodologies have been proposed this end. Among them, design element-spe...

The subject of this work is the application of fully discrete Galerkin finite element methods to initial-boundary value problems for linear partial integro-differential equations of parabolic type. We investigate numerical schemes based on the Padé discretization with respect to time and associated with certain quadrature formulas to approximate the integral term. A preliminary error estimate i...

This paper describes the development of an approximate method for propagating uncertainty through stochastic dynamical systems using a quadrature rule integration based method. The development of quadrature rules for Gaussian mixture distributions is discussed. A numerical solution to this problem is considered that uses a Gram-Schmidt process. Simulation results are presented where the quadrat...

By means of Sidi-Israeli’s quadrature rules, mechanical quadrature methods (MQMs) for solving the first kind boundary integral equations (BIEs) of steady state Stokes problem are presented. The convergence of numerical solutions by MQMs is proved based on Anselone’s collective compact and asymptotical compact theory, and the asymptotic expansions with the odd powers of the errors are provided, ...

In this paper we construct quadrature rules for the numerical evaluation of some singular integrals by using the interpolating-derivative splines. Convergence properties and numerical results are given.

We establish some companions of an Ostrowski type integral inequality for functions whose derivatives are absolutely continuous. Applications for composite quadrature rules are also given.

The extended Gaussian quadrature rules are shown to be an efficient tool for numerical integration of wide class of functions with singularities of logarithmic type. The quadratures are exact for the functions pol1n−1(x) + lnx pol2n−1(x) , where pol1n−1(x) and pol2n−1(x) are two arbitrary polynomials of degree n−1 and n is the order of the quadrature formula. We present an implementation of num...

We recall some results from a paper by Szego on a class of polynomials which are related to extended Gaussian quadrature rules. We show that a very efficient algorithm, for the computation of the abscissas of the rules in question, was already described in that paper. We also point out that this method extends to rules for integrals with an ultraspherical-type weight function. A bound for the e...