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

An Edge-Based Anisotropic Mesh Refinement Algorithm and Its Application to Interface Problems
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Year:    2010

Communications in Computational Physics, Vol. 8 (2010), Iss. 3 : pp. 511–540

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.210709.121109a

Communications in Computational Physics, Vol. 8 (2010), Iss. 3 : pp. 511–540

Published online:    2010-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    30

Keywords:   

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