A mesh optimization algorithm to decrease the maximum interpolation error of linear triangular finite elements

We present a mesh optimization algorithm for adaptively improving the finite element interpolation of a function of interest. The algorithm minimizes an objective function by swapping edges and moving nodes. Numerical experiments are performed on model problems. The results illustrate that the mesh...

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Bibliographic Details
Published inEngineering with computers Vol. 27; no. 1; pp. 3 - 15
Main Authors Hetmaniuk, U., Knupp, P.
Format Journal Article
LanguageEnglish
Published London Springer-Verlag 2011
Springer Nature B.V
Subjects
Algorithms
CAE) and Design
Calculus of Variations and Optimal Control; Optimization
Classical Mechanics
Computer Science
Computer-Aided Engineering (CAD
Control
Errors
Finite element method
Interpolation
Math. Applications in Chemistry
Mathematical analysis
Mathematical and Computational Engineering
Mathematical models
Norms
Optimization
Original Article
Systems Theory
Objective Function
Vertex Versus
Interpolation Error
Hessian Matrix
Inverted Element
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Summary:We present a mesh optimization algorithm for adaptively improving the finite element interpolation of a function of interest. The algorithm minimizes an objective function by swapping edges and moving nodes. Numerical experiments are performed on model problems. The results illustrate that the mesh optimization algorithm can reduce the W 1,∞ semi-norm of the interpolation error. For these examples, the L 2 , L ∞ , and H 1 norms decreased also.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:0177-0667
1435-5663
DOI:10.1007/s00366-010-0176-8