article

On optimal triangular meshes for minimizing the gradient error

Authors:

E. F. D'azevedo,

R. B. SimpsonAuthors Info & Claims

Numerische Mathematik, Volume 59, Issue 1

Pages 321 - 348

https://doi.org/10.1007/BF01385784

Published: 01 December 1991 Publication History

Abstract

Construction of optimal triangular meshes for controlling the errors in gradient estimation for piecewise linear interpolation of data functions in the plane is discussed. Using an appropriate linear coordinate transformation, rigorously optimal meshes for controlling the error in quadratic data functions are constructed. It is shown that the transformation can be generated as a curvilinear coordinate transformation for any C data function with nonsingular Hessian matrix. Using this transformation, a construction of nearly optimal meshes for general data functions is described and the error equilibration properties of these meshes discussed. In particular, it is shown that equilibration of errors is not a sufficient condition for optimality. A comparison of meshes generated under several different criteria is made, and their equilibrating properties illustrated.

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Published In

cover image Numerische Mathematik

Numerische Mathematik Volume 59, Issue 1

December 1991

838 pages

ISSN:0029-599X

Issue’s Table of Contents

Copyright © Copyright © 1991 Springer-Verlag.

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 December 1991

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Korotov SKřížek MKučera V(2022)On degenerating finite element tetrahedral partitionsNumerische Mathematik10.1007/s00211-022-01317-9152:2(307-329)Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s00211-022-01317-9
Laug PBorouchaki H(2017)Metric tensor recovery for adaptive meshingMathematics and Computers in Simulation10.1016/j.matcom.2015.02.004139:C(54-66)Online publication date: 1-Sep-2017
https://dl.acm.org/doi/10.1016/j.matcom.2015.02.004
Alauzet FLoseille A(2016)A decade of progress on anisotropic mesh adaptation for computational fluid dynamicsComputer-Aided Design10.1016/j.cad.2015.09.00572:C(13-39)Online publication date: 1-Mar-2016
https://dl.acm.org/doi/10.1016/j.cad.2015.09.005
Fortin ABriffard TGaron A(2015)A more efficient anisotropic mesh adaptation for the computation of Lagrangian coherent structuresJournal of Computational Physics10.1016/j.jcp.2015.01.010285:C(100-110)Online publication date: 15-Mar-2015
https://dl.acm.org/doi/10.1016/j.jcp.2015.01.010
Budd CRussell RWalsh E(2015)The geometry of r-adaptive meshes generated using optimal transport methodsJournal of Computational Physics10.1016/j.jcp.2014.11.007282:C(113-137)Online publication date: 1-Feb-2015
https://dl.acm.org/doi/10.1016/j.jcp.2014.11.007
Aubry RDey SMestreau EKaramete BGayman D(2015)A robust conforming NURBS tessellation for industrial applications based on a mesh generation approachComputer-Aided Design10.1016/j.cad.2014.12.00963:C(26-38)Online publication date: 1-Jun-2015
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Abgrall RBeaugendre HDobrzynski C(2014)An immersed boundary method using unstructured anisotropic mesh adaptation combined with level-sets and penalization techniquesJournal of Computational Physics10.5555/2743142.2743732257:PA(83-101)Online publication date: 15-Jan-2014
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Xie HYin X(2014)Metric tensors for the interpolation error and its gradient in L p normJournal of Computational Physics10.5555/2743139.2743543256:C(543-562)Online publication date: 1-Jan-2014
https://dl.acm.org/doi/10.5555/2743139.2743543
Jiao XColombi ANi XHart J(2010)Anisotropic mesh adaptation for evolving triangulated surfacesEngineering with Computers10.5555/3225288.322557926:4(363-376)Online publication date: 1-Aug-2010
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Kovacs DMyles AZorin DElber GFischer AKeyser JKim M(2010)Anisotropic quadrangulationProceedings of the 14th ACM Symposium on Solid and Physical Modeling10.1145/1839778.1839797(137-146)Online publication date: 1-Sep-2010
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