Commun. Comput. Phys., 8 (2010), pp. 511-540.


An Edge-Based Anisotropic Mesh Refinement Algorithm and its Application to Interface Problems

Duan Wang 1, Ruo Li 2*, Ningning Yan 3

1 LMAM and School of Mathematical Sciences, Peking University, 100871, Beijing, China.
2 CAPT, LMAM and School of Mathematical Sciences, Peking University, 100871, Beijing, China.
3 LSEC, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100080, Beijing, China.

Received 21 July 2009; Accepted (in revised version) 12 November 2009
Available online 15 April 2010
doi:10.4208/cicp.210709.121109a

Abstract

Based on an error estimate in terms of element edge vectors on arbitrary unstructured simplex meshes, we propose a new edge-based anisotropic mesh refinement algorithm. As the mesh adaptation indicator, the error estimate involves only the gradient of error rather than higher order derivatives. The preferred refinement edge is chosen to reduce the maximal term in the error estimate. The algorithm is implemented in both two- and three-dimensional cases, and applied to the singular function interpolation and the elliptic interface problem. The numerical results demonstrate that the convergence order obtained by using the proposed anisotropic mesh refinement algorithm can be higher than that given by the isotropic one.

AMS subject classifications: 65N22, 65N50, 65N55

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Key words: Adaptive finite element method, anisotropic mesh refinement, elliptic interface problem, non-homogeneous jump, a posteriori error estimate.

*Corresponding author.
Email: doreenwd@pku.edu.cn (D. Wang), rli@math.pku.edu.cn (R. Li), ynn@amss.ac.cn (N.-N. Yan)
 

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