Implementation of a meshless method for optimal control of elliptic variational inequality

In this paper, a mesh-free method is presented for the numerical solution of an optimal control problem constrained by an elliptic variational inequality. The proposed method is indirect and based on the element-free Galerkin method to solve the considered nonlinear optimal control problem. First, the optimality conditions of the problem are derived via the Lagrangian technique. The obtained conditions are mixed complementarity conditions which can be solved by specific efficient algorithms. Here, the moving least squares approximation is utilized within the element-free Galerkin approach to numerically solve the obtained optimality conditions. The proposed method is mesh-free and can be used with irregular meshes and even in irregular domains. Finally, The convergence of the proposed method is numerically investigated and results confirm high-order accuracy.

کلیدواژه ها:

optimal control problem ، Elliptic variational inequality ، Optimality conditions ، meshfree methods ، Element free Galerkin method