基于变域变分原理的一种有限元方法  

A New Finite Element Method Based on the Variable-domain Variational Principle

作　　者：段现报[1] 封卫兵[2] 

机构地区：[1]西安交通大学理学院,西安710049 [2]上海大学计算机工程与科学学院,上海200072

出　　处：《工程数学学报》2008年第1期44-52,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10371069)

摘　　要：本文从变域变分原理出发,提出了一种新的有限元方法,并将所提算法用于求解形状最优化问题。我们给出了最优化问题解的存在性及其离散形式。讨论了数值解的收敛性,给出了数值解与精确解之间的误差估计。最后给出了算法的具体实施步骤和一个具有代表性的数值算例,数值结果表明该算法是正确、高效的。Based on the variable-domain variational principle, we propose a new finite element method in the present paper. The proposed method is applied to the shape optimization problem. The existence of the solution and the discrete form of the optimization problem are given. The convergence and error estimate of the proposed algorithm are also provided. Finally, a representative numerical example is provided in order to illustrate the feasibility and efficiency of the new algorithm.

关 键 词：变域变分原理 有限元方法 议差估计 POISSON方程 

分 类 号：O242.21[理学—计算数学]