@Article{CiCP-37-498,
author = {Cai , YingGuo , Hailong and Zhang , Zhimin},
title = {Stabilized Continuous Linear Element Method for the Biharmonic Problems},
journal = {Communications in Computational Physics},
year = {2025},
volume = {37},
number = {2},
pages = {498--520},
abstract = {<p style="text-align: justify;">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&#39;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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0302},
url = {http://global-sci.org/intro/article_detail/cicp/23871.html}
}