CAJ | 학술논문

构造了一类四阶椭圆型变分不等式的双重网格投影法.首先利用罚方法将原变分不等式问题转换为一个非线性罚形式的变分方程;由Marchuk-Yanenko格式将罚方程转化为两个嵌套求解的子问题.针对两个子问题的求解网格不同,引入双重网格投影方法,建立了两种网格近似函数之间的联系;再利用Newton方法求解非线性方程.最后给出了数值算例,说明了方法的有效性.
구조료일류사계타원형변분불등식적쌍중망격투영법.수선이용벌방법장원변분불등식문제전환위일개비선성벌형식적변분방정;유Marchuk-Yanenko격식장벌방정전화위량개감투구해적자문제.침대량개자문제적구해망격불동,인입쌍중망격투영방법,건립료량충망격근사함수지간적련계;재이용Newton방법구해비선성방정.최후급출료수치산례,설명료방법적유효성.
A two-grid projection algorithm for a kind of elliptic variational inequality with fourth order was presented. First, the original problem was reduced to a nonlinear variational equation by the penalty method.Using Marchuk-Yanenko scheme, the penalised equation changed into two coupling sub-problems. As the numerical methods for these two sub-problems needed a different mesh, a projection between two different meshes was established, Newton method was used to solve the nonlinear equation. Finally the numerical example showed the efficiency of this method.