The effect of numerical quadrature in finite element methods for solving quasilinear elliptic problems of nonmonotone type is studied. Under similar assumption on the quadrature formula as for linear problems, optimal error estimates in the L2 and the H1 norms are proved. The numerical solution obtained from the finite element method with quadrature formula is shown to be unique for a sufficien...

1. Introduction. The estimation of quadrature errors for analytic functions has been considered by Davis and Rabinowitz [1]. An estimate for the error of the Gaussian quadrature formula for analytic functions was obtained by Davis [2]. McNamee [3] has also discussed the estimation of error of the Gauss-Legendre quadrature for analytic functions. Convergence of the Gaussian quadratures was discu...

A generalized N-point Birkhoff–Young quadrature of interpolatory type, with the Chebyshev weight, for numerical integration of analytic functions is considered. The nodes of such a quadrature are characterized by an orthogonality relation. Some special cases of this quadrature formula are derived. 2011 Elsevier Inc. All rights reserved.

We develop parallel one-dimensional globally adaptive quadrature algorithms, building on NAG code D01AKF. Our most eeective strategy replaces D01AKF's error estimate ranking strategy by a tabulation approach. D01AKF uses 61-point Gauss-Kronrod (GK) quadrature. We also use the 21-point GK rule. A fuller discussion, with expanded results, is given in 7].

We present a family of four-point quadrature rule, a generalization of Gauss-two point, Simpson’s 3/8, and Lobatto four-point quadrature rule for twice-differentiable mapping. Moreover, it is shown that the corresponding optimal quadrature formula presents better estimate in the context of four-point quadrature formulae of closed type. A unified treatment of error inequalities for different cla...