Year: 2020
Author: Yunqing Huang, Huayi Wei, Wei Yang, Nianyu Yi
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 1 : pp. 84–102
Abstract
We design and numerically validate a recovery based linear finite element method for solving the biharmonic equation. The main idea is to replace the gradient operator $\nabla$ on linear finite element space by $G(\nabla)$ in the weak formulation of the biharmonic equation, where $G$ is the recovery operator which recovers the piecewise constant function into the linear finite element space. By operator $G$, Laplace operator $\Delta$ is replaced by $\nabla\cdot G(\nabla)$. Furthermore, the boundary condition on normal derivative $\nabla u\cdot \pmb{n}$ is treated by the boundary penalty method. The explicit matrix expression of the proposed method is also introduced. Numerical examples on the uniform and adaptive meshes are presented to illustrate the correctness and effectiveness of the proposed method.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1902-m2018-0187
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 1 : pp. 84–102
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Biharmonic equation Linear finite element Recovery Adaptive.
Author Details
-
A Hessian recovery-based finite difference method for biharmonic problems
Xu, Minqiang | Shi, ChungangApplied Mathematics Letters, Vol. 137 (2023), Iss. P.108503
https://doi.org/10.1016/j.aml.2022.108503 [Citations: 4] -
A Mathematical Analysis Method for Bending Problem of Clamped Shallow Spherical Shell on Elastic Foundation
Li, Shanqing | Yang, Chunsheng | Xia, Fengfei | Yuan, HongInternational Journal of Computational Methods, Vol. 19 (2022), Iss. 07
https://doi.org/10.1142/S0219876221410164 [Citations: 0] -
Numerical solution of the cavity scattering problem for flexural waves on thin plates: Linear finite element methods
Yue, Junhong | Li, PeijunJournal of Computational Physics, Vol. 497 (2024), Iss. P.112606
https://doi.org/10.1016/j.jcp.2023.112606 [Citations: 0] -
A new recovery based C0 element method for fourth-order equations
Cui, Yuanquan | Jia, Yuntao | Zhang, Jinrui | Niu, JingApplied Mathematics Letters, Vol. 147 (2024), Iss. P.108858
https://doi.org/10.1016/j.aml.2023.108858 [Citations: 0]