关于变分不等式问题近似解的数值证明(英文)  

Numerical verification of approximate solutions for variational inequalities

作　　者：胡淑娟[1] 王希营[1] 丁方允[1] 

机构地区：[1]兰州大学数学系,兰州730000

出　　处：《计算力学学报》2006年第1期40-45,共6页Chinese Journal of Computational Mechanics

基　　金：兰州大学交叉学科青年创新研究基金(LZU200308)资助项目~~

摘　　要：基于文献[1]给出了一种数值证明变分不等式解的存在性方法。通过Hilbert空间中的Riesz表示定理,首先将变分不等式问题的迭代过程转化为一种不动点形式,再利用Schauder不动点定理构造了一个高效率的数值证明过程,即通过数值计算产生一个包含近似解的有界闭凸子集。非线性Helmholtz方程的算例说明这一方法的可行性和高效性。In this paper, a numerical method to verify the existence of solutions for variational inequalities is presented. This method is based on the work of reference [1]. By using the Riesz present theory in Hilbert space, we first transform the iterative procedure of variational inequalities into a fixed point form. Then, using the Schauder fixed point theory, we construct a numerical verification method with high efficiency that through numerical computation generates a bounded, closed, convex set in which the approximate solution is included. Finally, a numerical example for nonlinear Helmholtz equation is presented.

关 键 词：变分不等式 不动点迭代 迭代解集 不动点定理 数值证明 

分 类 号：O241[理学—计算数学]