Adaptive finite element analysis of elliptic problems based on bubble-type local mesh generation

Zhang, Weiwie, Nie, Yufeng, & Gu, YuanTong (2015) Adaptive finite element analysis of elliptic problems based on bubble-type local mesh generation. Journal of Computational and Applied Mathematics, 280, pp. 42-58.

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A new mesh adaptivity algorithm that combines a posteriori error estimation with bubble-type local mesh generation (BLMG) strategy for elliptic differential equations is proposed. The size function used in the BLMG is defined on each vertex during the adaptive process based on the obtained error estimator. In order to avoid the excessive coarsening and refining in each iterative step, two factor thresholds are introduced in the size function. The advantages of the BLMG-based adaptive finite element method, compared with other known methods, are given as follows: the refining and coarsening are obtained fluently in the same framework; the local a posteriori error estimation is easy to implement through the adjacency list of the BLMG method; at all levels of refinement, the updated triangles remain very well shaped, even if the mesh size at any particular refinement level varies by several orders of magnitude. Several numerical examples with singularities for the elliptic problems, where the explicit error estimators are used, verify the efficiency of the algorithm. The analysis for the parameters introduced in the size function shows that the algorithm has good flexibility.

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ID Code: 79675
Item Type: Journal Article
Refereed: Yes
Keywords: Mesh size function, Node placement, Local mesh generation, Error estimator, Adaptive analysis
DOI: 10.1016/
ISSN: 0377-0427
Subjects: Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > MECHANICAL ENGINEERING (091300) > Numerical Modelling and Mechanical Characterisation (091307)
Divisions: Current > Schools > School of Chemistry, Physics & Mechanical Engineering
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2014 Elsevier B.V.
Copyright Statement: NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational and Applied Mathematics, Volume 280, (15 May 2015), DOI: 10.1016/
Deposited On: 05 Jan 2015 02:32
Last Modified: 12 Jan 2015 01:36

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