Journal article

Gradient Recovery for Elliptic Interface Problem: I. Body-Fitted Mesh

Hailong Guo, Xu Yang

COMMUNICATIONS IN COMPUTATIONAL PHYSICS | GLOBAL SCIENCE PRESS | Published : 2018

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.

University of Melbourne Researchers

Grants

Awarded by NSF


Awarded by KI-Net NSF RNMS


Funding Acknowledgements

We thank anonymous referees for valuable suggestions and comments. This work was partially supported by the NSF grant DMS-1418936, KI-Net NSF RNMS grant 1107291, and Hellman Family Foundation Faculty Fellowship, UC Santa Barbara.