RECOVERY BASED FINITE ELEMENT METHOD FOR BIHARMONIC EQUATION IN 2D |
| |
Authors: | Yunqing Huang Huayi Wei Wei Yang & Nianyu Yi |
| |
Institution: | Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education,School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China;Hunan Key Laboratory for Computation and Simulation in Science and Engineering;School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China |
| |
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. |
| |
Keywords: | Biharmonic equation Linear finite element Recovery Adaptive |
本文献已被 维普 万方数据 等数据库收录! |
| 点击此处可从《计算数学(英文版)》浏览原始摘要信息 |
|