In this paper, we derive a general accuracy-preserving boundary flux quadrature formula for the secondand third-order node-centered edge-based finite-volume discretizations on triangular and tetrahedral grids. It is demonstrated that the general formula reduces to some well-known formulas for the second-order scheme in the case of linear fluxes. Some special boundary grids are also examined. In...

The Filon formula is advantageous over usual numerical integration formulas for smooth fix), especially for large k, since the number of points which need be tabulated depends on the behavior of fix) rather than on fix) sin kx or fix) cos kx. Under certain circumstances the Filon quadrature formula reduces to a simple form, namely (2) S* = ii-l)m/k){fia) fib)} , C* = ii-l)m/k)[fib) fia)} , wher...

The idea of Gauss–Kronrod quadrature, in a germinal form, is traced back to an 1894 paper of R. Skutsch. The idea of inserting n+1 nodes into an n-point Gaussian quadrature rule and choosing them and the weights of the resulting (2n+1)-point quadrature rule in such a manner as to maximize the polynomial degree of exactness is generally attributed to A.S. Kronrod [2], [3]. This is entirely justi...

Abstract This paper studies the problem of construction of optimal quadrature formulas in the sense of Sard in the space ( ) 2 (0,1) m L . In this paper the quadrature sum consists of values of the integrand and its first derivative at nodes. The coefficients of optimal quadrature formulas are found and the norm of the optimal error functional is calculated for arbitrary natural number 1 N m ≥ ...