TY - JOUR
T1 - Stabilized Continuous Linear Element Method for the Biharmonic Problems
AU - Cai , Ying
AU - Guo , Hailong
AU - Zhang , Zhimin
JO - Communications in Computational Physics
VL - 2
SP - 498
EP - 520
PY - 2025
DA - 2025/02
SN - 37
DO - http://doi.org/10.4208/cicp.OA-2023-0302
UR - https://global-sci.org/intro/article_detail/cicp/23871.html
KW - Biharmonic problems, gradient recovery, superconvergence, linear finite element.
AB - <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>