一类四阶椭圆型变分不等式的二重网格算法

A two-grid projection algorithm for a kind of elliptic variational inequality with fourth order

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。

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.