Journal Article10.1007/S00366-010-0176-8
A mesh optimization algorithm to decrease the maximum interpolation error of linear triangular finite elements
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TL;DR: The results illustrate that the mesh optimization algorithm can reduce the W1,∞ semi-norm of the interpolation error, and the L2, L∞, and H1 norms decreased also.
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Abstract: 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.
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Citations
A fully optimal anisotropic mesh adaptation method based on a hierarchical error estimator
TL;DR: A new two-dimensional mesh adaptation method which produces optimal meshes for all quadratic functions, positive definite or indefinite, and it is shown that the optimal mesh depends only on the solution itself and very little on the differential operator of the problem at hand.
32
Adaptation de maillages anisotropes par un estimateur d'erreur hiérarchique
Richard Bois
- 01 Jan 2012
TL;DR: In this article, a hierarchical error estimator for mesh adaptation is presented. But it is not a hierarchical estimator that can be used in a mesh adaptation algorithm to obtain a more accurate approximation to the solution of a partial differential equation.
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Evaluating Airfoil Mesh Quality with Transformer
Zhixiang Liu,Huan Liu,Yuanji Chen,Wenbo Zhang,Wei Song,Liping Zhou,Quanmiao Wei,Jingxiang Xu +7 more
TL;DR: In this paper , a Transformer-based network for automatic mesh quality evaluation (Gridformer) is proposed, which can automatically identify mesh integrity quality defects and has advantages in computational efficiency and prediction accuracy compared to widely used neural networks.
Edge-based anisotropic mesh adaptation of unstructured meshes with applications to compressible flows
TL;DR: An adaptation procedure using refinement, coarsening and smoothing with anisotropic considerations for unstructured meshes and its coupling with a compressible flow solver is presented in this work.
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