Year: 2018
Communications in Computational Physics, Vol. 23 (2018), Iss. 5 : pp. 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2017-0026
Communications in Computational Physics, Vol. 23 (2018), Iss. 5 : pp. 1488–1511
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Elliptic interface problem gradient recovery superconvergence body-fitted mesh a posteriori error estimator adaptive method.
-
Enriched gradient recovery for interface solutions of the Poisson-Boltzmann equation
Borleske, George | Zhou, Y.C.Journal of Computational Physics, Vol. 421 (2020), Iss. P.109725
https://doi.org/10.1016/j.jcp.2020.109725 [Citations: 1] -
A flux-jump preserved gradient recovery technique for accurately predicting the electrostatic field of an immersed biomolecule
Li, Jiao | Ying, Jinyong | Lu, BenzhuoJournal of Computational Physics, Vol. 396 (2019), Iss. P.193
https://doi.org/10.1016/j.jcp.2019.06.049 [Citations: 6] -
Flux recovery scheme for elliptic interface problems
El-Agamy, M. | Essam, R. | Elsaid, A.Alexandria Engineering Journal, Vol. 62 (2023), Iss. P.303
https://doi.org/10.1016/j.aej.2022.07.028 [Citations: 3] -
A three-dimensional Petrov-Galerkin finite element interface method for solving inhomogeneous anisotropic Maxwell's equations in irregular regions
Zhao, Meiling | Shi, Jieyu | Wang, LiqunComputers & Mathematics with Applications, Vol. 152 (2023), Iss. P.364
https://doi.org/10.1016/j.camwa.2023.10.035 [Citations: 1] -
Unfitted Nitsche’s Method for Computing Wave Modes in Topological Materials
Guo, Hailong | Yang, Xu | Zhu, YiJournal of Scientific Computing, Vol. 88 (2021), Iss. 1
https://doi.org/10.1007/s10915-021-01540-w [Citations: 1] -
Superconvergence of unfitted Rannacher-Turek nonconforming element for elliptic interface problems
He, Xiaoxiao | Chen, Yanping | Ji, Haifeng | Wang, HaijinApplied Numerical Mathematics, Vol. 203 (2024), Iss. P.32
https://doi.org/10.1016/j.apnum.2024.05.016 [Citations: 1]