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Volume 23, Issue 5
Gradient Recovery for Elliptic Interface Problem: I. Body-Fitted Mesh

Hailong Guo & Xu Yang

DOI: 10.4208/cicp.OA-2017-0026

Commun. Comput. Phys., 23 (2018), pp. 1488-1511.

Published online: 2018-08

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  • Abstract

In this paper, we propose a new gradient recovery method for elliptic interface problem using body-fitted meshes. Due to the lack of regularity of the solution at the interface, standard gradient recovery methods fail to give superconvergent results and thus will lead to overrefinement when served as a posteriori error estimators. This drawback is overcome by designing a new gradient recovery operator. We prove the superconvergence of the new method on both mildly unstructured meshes and adaptive meshes. Several numerical examples are presented to verify the superconvergence and its robustness as a posteriori error estimator.

  • Keywords

Elliptic interface problem, gradient recovery, superconvergence, body-fitted mesh, a posteriori error estimator, adaptive method.

  • AMS Subject Headings

65L10, 65L60, 65L70

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-23-1488, author = {Hailong Guo and Xu Yang}, title = {Gradient Recovery for Elliptic Interface Problem: I. Body-Fitted Mesh}, journal = {Communications in Computational Physics}, year = {2018}, volume = {23}, number = {5}, pages = {1488--1511}, abstract = {

In this paper, we propose a new gradient recovery method for elliptic interface problem using body-fitted meshes. Due to the lack of regularity of the solution at the interface, standard gradient recovery methods fail to give superconvergent results and thus will lead to overrefinement when served as a posteriori error estimators. This drawback is overcome by designing a new gradient recovery operator. We prove the superconvergence of the new method on both mildly unstructured meshes and adaptive meshes. Several numerical examples are presented to verify the superconvergence and its robustness as a posteriori error estimator.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0026}, url = {http://global-sci.org/intro/article_detail/cicp/12630.html} }
TY - JOUR T1 - Gradient Recovery for Elliptic Interface Problem: I. Body-Fitted Mesh AU - Hailong Guo & Xu Yang JO - Communications in Computational Physics VL - 5 SP - 1488 EP - 1511 PY - 2018 DA - 2018/08 SN - 23 DO - http://doi.org/10.4208/cicp.OA-2017-0026 UR - https://global-sci.org/intro/article_detail/cicp/12630.html KW - Elliptic interface problem, gradient recovery, superconvergence, body-fitted mesh, a posteriori error estimator, adaptive method. AB -

In this paper, we propose a new gradient recovery method for elliptic interface problem using body-fitted meshes. Due to the lack of regularity of the solution at the interface, standard gradient recovery methods fail to give superconvergent results and thus will lead to overrefinement when served as a posteriori error estimators. This drawback is overcome by designing a new gradient recovery operator. We prove the superconvergence of the new method on both mildly unstructured meshes and adaptive meshes. Several numerical examples are presented to verify the superconvergence and its robustness as a posteriori error estimator.

Hailong Guo and Xu Yang. (2018). Gradient Recovery for Elliptic Interface Problem: I. Body-Fitted Mesh. Communications in Computational Physics. 23 (5). 1488-1511. doi:10.4208/cicp.OA-2017-0026
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