Year: 2025
Author: Ying Cai, Hailong Guo, Zhimin Zhang
Communications in Computational Physics, Vol. 37 (2025), Iss. 2 : pp. 498–520
Abstract
In this paper, we introduce a new stabilized continuous linear element method for solving biharmonic problems. Leveraging the gradient recovery operator, we reconstruct the discrete Hessian for piecewise continuous linear functions. By adding a stability term to the discrete bilinear form, we bypass the need for the discrete Poincaré inequality. We employ Nitsche's method for weakly enforcing boundary conditions. We establish well-posedness of the solution and derive optimal error estimates in energy and $L^2$ norms. Numerical results are provided to validate our theoretical findings.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0302
Communications in Computational Physics, Vol. 37 (2025), Iss. 2 : pp. 498–520
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Biharmonic problems gradient recovery superconvergence linear finite element.