A fourth-order variational inequality of the second kind arising in a plate frictional bending problem is considered. By using regularization method, the original problem can be formulated as a differentiable variatio...A fourth-order variational inequality of the second kind arising in a plate frictional bending problem is considered. By using regularization method, the original problem can be formulated as a differentiable variational equation, and the corresponding discrete FEM variational equation is presented afterwards. Abstract error estimates and error estimates of the approximation are derived in terms of energy norm and L^2-norm.展开更多
The authors first prove a convergence result on the Ka(?)anov method for solving generalnonlinear variational inequalities of the second kind and then apply the Kacanov method tosolve a nonlinear variational inequalit...The authors first prove a convergence result on the Ka(?)anov method for solving generalnonlinear variational inequalities of the second kind and then apply the Kacanov method tosolve a nonlinear variational inequality of the second kind arising in elastoplasticity. In additionto the convergence result, an a posteriori error estimate is shown for the Kacanov iterates. Ineach step of the Ka(?)anov iteration, one has a (linear) variational inequality of the secondkind, which can be solved by using a regularization technique. The Ka(?)anov iteration andthe regularization technique together provide approximations which can be readily computednumerically. An a posteriori error estimate is derived for the combined effect of the Ka(?)anoviteration and the regularization.展开更多
We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove ...We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove the strong convergence of the optimal control and state systems associated to this family to a similar optimal control problem. This work solves the open problem left by the authors in IFIP TC7 CSMO2011.展开更多
基金Supported by the National Natural Science Foundation of China(10201026,10672111)
文摘A fourth-order variational inequality of the second kind arising in a plate frictional bending problem is considered. By using regularization method, the original problem can be formulated as a differentiable variational equation, and the corresponding discrete FEM variational equation is presented afterwards. Abstract error estimates and error estimates of the approximation are derived in terms of energy norm and L^2-norm.
基金Project supported by the ONR grant N00014-90-J-1238
文摘The authors first prove a convergence result on the Ka(?)anov method for solving generalnonlinear variational inequalities of the second kind and then apply the Kacanov method tosolve a nonlinear variational inequality of the second kind arising in elastoplasticity. In additionto the convergence result, an a posteriori error estimate is shown for the Kacanov iterates. Ineach step of the Ka(?)anov iteration, one has a (linear) variational inequality of the secondkind, which can be solved by using a regularization technique. The Ka(?)anov iteration andthe regularization technique together provide approximations which can be readily computednumerically. An a posteriori error estimate is derived for the combined effect of the Ka(?)anoviteration and the regularization.
基金partly supported by the Institut Camille Jordan ST-Etienne Universitythe projects Argentine ANPCyT PICTO Austral 2008 # 73 and SOARD-AFOSR (No. FA9550-10-1-0023)
文摘We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove the strong convergence of the optimal control and state systems associated to this family to a similar optimal control problem. This work solves the open problem left by the authors in IFIP TC7 CSMO2011.
