University of Guilan Journal of Mathematical Modeling 2345-394X 2026 02 09 Implementation of a meshless method for Optimal control of elliptic variational inequality 9426 10.22124/jmm.2026.31996.2891 EN Mahmood Khaksar-e Oshagh Department of mathematics education, Farhangian University, Tehran University Journal Article 2025 10 16 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.<br />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.<br />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.<br />Finally, The convergence of the proposed method is numerically investigated and results confirm high-order accuracy. https://jmm.guilan.ac.ir/article_9426_a2728daaa71cc4d3485412bc73677c8f.pdf