Year: 2019
Author: Wei Guo, Yufeng Nie, Weiwei Zhang
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 5 : pp. 745–766
Abstract
A new anisotropic adaptive mesh refinement method based on anisotropic bubble-type local mesh generation (ABLMG) for elliptic partial differential equations is proposed. The anisotropic meshes are generated as quasi-uniform meshes in metric spaces with the metric determined on each vertex by anisotropic a posteriori error estimator. Under the new metric, the error is equidistributed in the directions of maximum and minimum stretching on an element, and the mesh size is reduced/coarsened in regions with large/small errors. With the full use of the adjacent lists provided by the node placement method, the local mesh for each vertex is generated through ABLMG method. Compared with other methods, the mesh refining and coarsening can be obtained in the same framework and the mesh suits the metric well at each refinement level. Numerical results in two-dimensions are presented to verify the ability of our metric tensor to generate anisotropic mesh with correct concentration and stretching direction.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2019-IJNAM-13252
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 5 : pp. 745–766
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Metric tensor anisotropic mesh adaptive finite element node placement and local mesh generation.