An adaptive numerical integration algorithm for polygons

DOI10.1016/j.apnum.2009.11.001zbMath1189.65048OpenAlexW2012762834MaRDI QIDQ969310

Chong-Jun Li, Cattarina Dagnino

Publication date: 6 May 2010

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2009.11.001

zbMATH Keywords

performanceconvergencenumerical examplesadaptive algorithmGaussian rulesspline finite elementGreen's integral formulanumerical cubaturetriangulated quadrangulation

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (4)

Polynomial interpolation and cubature over polygons ⋮ Numerical integration based on trivariate \(C ^{2}\) quartic spline quasi-interpolants ⋮ Finite-part integrals over polygons by an 8-node quadrilateral spline finite element ⋮ A meshless like method for the approximate solution of integral equations over polygons

Uses Software

• DCUTRI
• adsimp

Cites Work

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• Scattered data interpolation and approximation using bivariate \(C^{1}\) piecewise cubic polynomials
• Numerical integration over polygons using an eight-node quadrilateral spline finite element
• Product Gauss cubature over polygons based on Green's integration formula
• Adaptive cubature over a collection of triangles using the \(d\)- transformation
• Converting triangulations to quadrangulations
• An encyclopaedia of cubature formulas.
• Experimental results on quadrangulations of sets of fixed points
• A new 8-node quadrilateral spline finite element
• A quadrilateral finite element including vertex rotations for plane elasticity analysis
• Algorithm 706: DCUTRI: an algorithm for adaptive cubature over a collection of triangles
• An adaptive numerical cubature algorithm for simplices

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