Extended Multidimensional Integration Formulas on Polytope Meshes

DOI10.1137/18M1234564WikidataQ127023684 ScholiaQ127023684MaRDI QIDQ5240805

Boris Semisalov, Allal Guessab

Publication date: 29 October 2019

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

convexityapproximationcubature formulascentroidal Voronoi tessellationbest error estimatessingularity of integrand

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18)

Related Items (3)

Optimal general Hermite-Hadamard-type inequalities in a ball and their applications in multidimensional numerical integration ⋮ A characterization for the validity of the Hermite-Hadamard inequality on a simplex ⋮ On the improvement of the triangular Shepard method by non conformal polynomial elements

Uses Software

• PolyMesher

Cites Work

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• Characterization of the existence of an enriched linear finite element approximation using biorthogonal systems
• \texttt{PolyMesher}: a general-purpose mesh generator for polygonal elements written in Matlab
• Numerical integration of homogeneous functions on convex and nonconvex polygons and polyhedra
• New cubature formulas and Hermite-Hadamard type inequalities using integrals over some hyperplanes in the \(d\)-dimensional hyper-rectangle
• A multivariate version of Hammer's inequality and its consequences in numerical integration
• Numerical integration using integrals over hyperplane sections of simplices in a triangulation of a polytope
• An extended family of nonconforming quasi-Wilson elements for solving elasticity problem
• Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
• Integration on a convex polytope
• Centroidal Voronoi Tessellations: Applications and Algorithms
• Convexity results and sharp error estimates in approximate multivariate integration
• A simple necessary and sufficient condition for the enrichment of the Crouzeix-Raviart element
• A Unified and General Framework for Enriching Finite Element Approximations
• Unified edge-oriented stabilization of nonconforming FEM for incompressible flow problems: Numerical investigations

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