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| 椭圆型方程的一种新型混合有限元格式 | |
| 引用本文： | 史峰,于佳平,李开泰. 椭圆型方程的一种新型混合有限元格式[J]. 工程数学学报, 2011, 28(2): 231-237 |
| 作者姓名： | 史峰 于佳平 李开泰 |
| 作者单位： | 西安交通大学理学院; |
| 基金项目： | 国家自然科学基金(10971165;10771167;10926080)~~ |
| 摘 要： | 基于实际问题对通量较低的正则性要求,本文建立了椭圆型方程的一种新型混合变分形式.在鞍点问题框架下,通过验证LBB条件,证明了该混合形式解的存在唯一性.由于压力空间不再是传统的H(div),而是平方可积空间,因此混合元的选取变得简单容易.同时本文给出了相应的有限元逼近形式,并对于由分片常数速度元和分片线性压力元构成的协调... |
| 关 键 词： | 椭圆型方程 混合变分形式 协调有限元对 LBB条件 |
A New Mixed Finite Element Scheme for Elliptic Equations |
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| SHI Feng,YU Jia-ping,LI Kai-tai. A New Mixed Finite Element Scheme for Elliptic Equations[J]. Chinese Journal of Engineering Mathematics, 2011, 28(2): 231-237 | |
| Authors: | SHI Feng YU Jia-ping LI Kai-tai |
| Affiliation: | SHI Feng,YU Jia-ping,LI Kai-tai (School of Science,Xi'an Jiaotong University,Xi'an 710049) |
| Abstract: | In this paper,a new mixed variational formulation to the elliptic equation is given based on the less regularity of flux in practical problems,and the existence and uniqueness of solution to this formulation is shown under the framework of the saddle point problem by verifying the LBB condition.Since in the new mixed variational formulation,the pressure belongs to the square integrable space instead of the classical H (div),the choices of finite element pairs become simple and easy.Based on this new formula... |
| Keywords: | elliptic equation mixed variational formulation conforming finite element pair LBB condition |
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