Superconvergence of Differential Structure for Finite Element Methods on Perturbed Surface Meshes

Authors

DOI:

https://doi.org/10.4208/jcm.2404-m2023-0245

Keywords:

Superconvergenc, Differential structure, Discretized surfaces with deviation, Geometric supercloseness, Gradient recovery

Abstract

Superconvergence of differential structure on discretized surfaces is studied in this paper. The newly introduced geometric supercloseness provides us with a fundamental tool to prove the superconvergence of gradient recovery on deviated surfaces. An algorithmic framework for gradient recovery without exact geometric information is introduced. Several numerical examples are documented to validate the theoretical results.

Author Biographies

  • Guozhi Dong

    School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha 410083, China

  • Hailong Guo

    School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, 3010, Australia

  • Ting Guo

    Key Laboratory of CSM (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China

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Published

2025-10-30

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Issue

Vol. 43 No. 6 (2025)

Section

Articles

How to Cite

Superconvergence of Differential Structure for Finite Element Methods on Perturbed Surface Meshes. (2025). Journal of Computational Mathematics, 43(6), 1374-1396. https://doi.org/10.4208/jcm.2404-m2023-0245