一类非线性变分不等式的罚有限元法

一类非线性变分不等式的罚有限元法 PENALTY-FINITE ELEMENT METHOD FOR A CLASS OF NONLINEAR VARIATIONAL INEQUALITIES 李茂祥 Li Maoxiang 1 first-author 武汉大学数学系 武汉大学数学系 Department of Mathematics,Wuhan University Department of Mathematics,Wuhan University 本文讨论用罚有限元方法来求解一类非线性变分不等式 < Au,v-u > :≥ < f,v-u > ,这里 Au=-sum from n to i-1 a x,u,▽u +a o （x,u,▽u）。并证明逼近解的收敛性。这类问题比文[4]所研究过的要广泛一些。本文后部分还用迭代罚函数方法讨论了一类非线性拟变分不等式。在一定条件下,证明了这类拟变分不等式存在唯一解,同样也证明了其逼近序列的收敛性。关键词非线性变分不等式非线性拟变分不等式罚有限元法迭代罚函数法逼近解的收敛性 In this paper,we have discusseda class of nonliear variational inequalities and their approximations by penalty-finite element method.The convergences have been proved.Existence solution for a class of guasi variational inequalities is investigated by iterative penalty function method.Moreover,we showed that approximate sequences conveges to the solution of the QVI mono- tonically from above. 非线性变分不等式 非线性拟变分不等式 罚有限元法 迭代罚函数法 逼近解的收敛性 Nonlinear variational inequalities Nonlinear quasi variational inequalities Penalty finite element method Iteratiue penalty function method Convergence of approximate sequences 1990-02-01 2021-04-01 2