New a posteriori error indicators based on edgewise slope-limiting are presented. The L2-norm is employed to measure the error of the solution gradient in both global and element sense. A second order Newton-Cotes formula is utilized in order to decompose the local gradient error from a P1-finite element solution into a sum of edge contributions. The gradient values at edge midpoints are interp...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 4 January 2021Accepted: 07 June 2021Published online: 03 February 2022KeywordsGauss quadrature, Gauss--Hermite, Newton--Cotes, Clenshaw--Curtis, cubatureAMS Subject Headings41A55, 65D32Publication DataISSN (print): 0036-1445ISSN (online): 1095-7200Publisher: Society for I...

The thermal management of a system needs an accurate and efficient measurement exergy. For optimal performance, entropy should be minimized. This study explores the enhancement exchange in stream Eyring–Powell fluid comprising nanoparticles saturating vertical oriented dual cylindrical domain with uniform conductivity viscous dissipation effects. A symmetrical sine wave over walls is used to in...

hybrid of rationalized haar functions are developed to approximate the solution of the differential equations. the properties of hybrid functions which are the combinations of block-pulse functions and rationalized haar functions are first presented. these properties together with the newton-cotes nodes are then utilized to reduce the differential equations to the solution of algebraic equation...

Accurate numericalintegrationof singularfunctions usually requireseither adaptivity or product integration. Both interfere with fast summation techniques and thus hamper large-scale computations. This paper presents a method for computing highly accurate quadrature formulas for singular functions which combine well with fast summation methods. Given the singularity and the N nodes, we rst const...

An efficient implementation of the high-order spectral volume (SV) method is presented for multi-dimensional conservation laws on unstructured grids. In the SV method, each simplex cell is called a spectral volume (SV), and the SV is further subdivided into polygonal (2D), or polyhedral (3D) control volumes (CVs) to support high-order data reconstructions. In the traditional implementation, Gau...

The Gauss-Kronrod quadrature scheme, which is based on the zeros of Legendre polynomials and Stieltjes polynomials, is the standard method for automatic numerical integration in mathematical software libraries. For a long time, very little was known about the error of the Gauss-Kronrod scheme. An essential progress was made only recently, based on new bounds and as-ymptotic properties for the S...