Greedy bisection generates optimally adapted triangulations

DOI10.1090/S0025-5718-2011-02459-2zbMath1252.65043arXiv1101.1452OpenAlexW3105118373MaRDI QIDQ5389434

Albert Cohen, Jean-Marie Mirebeau

Publication date: 26 April 2012

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.1452

zbMATH Keywords

finite element approximationerror estimateanisotropic triangulationgreedy bisection algorithmnon-conforming triangulation

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Computer-aided design (modeling of curves and surfaces) (65D17)

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Adaptive anisotropic Petrov-Galerkin methods for first order transport equations, Anisotropic Triangulation Methods in Adaptive Image Approximation, Red–green refinement of simplicial meshes in $d$ dimensions, An Adaptive Triangulation Method for Bivariate Spline Solutions of PDEs, Constructive approximation on graded meshes for the integral fractional Laplacian, Adaptive multiresolution analysis based on anisotropic triangulations, Introduction to vector quantization and its applications for numerics, Optimal $N$-term approximation by linear splines over anisotropic Delaunay triangulations, Efficient Resolution of Anisotropic Structures

Cites Work

• Optimal anisotropic meshes for minimizing interpolation errors in $L^p$-norm
• Adaptive multiresolution analysis based on anisotropic triangulations
• On the Error of Linear Interpolation and the Orientation, Aspect Ratio, and Internal Angles of a Triangle
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