计算力学学报
計算力學學報
계산역학학보
CHINESE JOURNAL OF COMPUTATIONAL MECHANICS
2006年
1期
40-45
,共6页
交分不等式%不动点迭代%迭代解集%不动点定理%数值证明
交分不等式%不動點迭代%迭代解集%不動點定理%數值證明
교분불등식%불동점질대%질대해집%불동점정리%수치증명
variational inequality%fixed point iteration%iterative solution set%fixed point theorem%numerical verification
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.
基于文獻[1]給齣瞭一種數值證明變分不等式解的存在性方法.通過Hilbert空間中的Riesz錶示定理,首先將變分不等式問題的迭代過程轉化為一種不動點形式,再利用Schauder不動點定理構造瞭一箇高效率的數值證明過程,即通過數值計算產生一箇包含近似解的有界閉凸子集.非線性Helmholtz方程的算例說明這一方法的可行性和高效性.
기우문헌[1]급출료일충수치증명변분불등식해적존재성방법.통과Hilbert공간중적Riesz표시정리,수선장변분불등식문제적질대과정전화위일충불동점형식,재이용Schauder불동점정리구조료일개고효솔적수치증명과정,즉통과수치계산산생일개포함근사해적유계폐철자집.비선성Helmholtz방정적산례설명저일방법적가행성화고효성.
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.
