Variational Mesh Adaptation: Isotropy and Equidistribution

doi:10.1006/jcph.2001.6945

Journal of Computational Physics

Volume 174, Issue 2, 10 December 2001, Pages 903-924

https://doi.org/10.1006/jcph.2001.6945 Get rights and content

Abstract

We present a new approach for developing more robust and error-oriented mesh adaptation methods. Specifically, assuming that a regular (in cell shape) and uniform (in cell size) computational mesh is used (as is commonly done in computation), we develop a criterion for mesh adaptation based on an error function whose definition is motivated by the analysis of function variation and local error behavior for linear interpolation. The criterion is then decomposed into two aspects, the isotropy (or conformity) and uniformity (or equidistribution) requirements, each of which can be easier to deal with. The functionals that satisfy these conditions approximately are constructed using discrete and continuous inequalities. A new functional is finally formulated by combining the functionals corresponding to the isotropy and uniformity requirements. The features of the functional are analyzed and demonstrated by numerical results. In particular, unlike the existing mesh adaptation functionals, the new functional has clear geometric meanings of minimization. A mesh that has the desired properties of isotropy and equidistribution can be obtained by properly choosing the values of two parameters. The analysis presented in this article also provides a better understanding of the increasingly popular method of harmonic mapping in two dimensions.

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Citation Excerpt :
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Regular ArticleVariational Mesh Adaptation: Isotropy and Equidistribution

Abstract

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J. Comput. Phys.

J. Comput. Phys.

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Least squares and approximate equidistribution in multidimensions

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SIAM J. Sci. Stat. Comput.

On optimal triangular meshes for minimizing the gradient error

Numer. Math.

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Regular Article
Variational Mesh Adaptation: Isotropy and Equidistribution