University of Guilan Journal of Mathematical Modeling 2345-394X 13 4 2025 12 01 Numerical solution of obstacle problem by using the mesh-free radial point interpolation method 929 942 8877 10.22124/jmm.2025.29905.2671 EN Ahmed Awad Nasser Department of Mathematics, Isfahan (Khorasgan) branch, Islamic Azad University, Isfahan, Iran Masoud Allame Department of Mathematics, Isfahan (Khorasgan) branch, Islamic Azad University, Isfahan, Iran Habeeb Abed Kadhim Aal-Rkhais Department of Mathematics, College of Computer and Mathematics, University of Thi-Qar, Iraq Majid Tavassoli-Kajani Department of Mathematics, Isfahan (Khorasgan) branch, Islamic Azad University, Isfahan, Iran Journal Article 2025 03 07 The obstacle problem is a well-known type of elliptic variational inequality that originally arose from contact issues in solid mechanics. The solutions to the obstacle problem often have irregularities along a free boundary, which can be effective in designing an appropriate numerical method for these problems.  In this paper, we present a  mesh-free method based on the radial point interpolation method for numerically solving an obstacle problem. In the proposed method, the  radial point interpolating shape functions are utilized in the global weak form of the obstacle problem, based on the element-free Galerkin method. This approach is combined with an active set strategy to address the obstacle problem. One of the key benefits of the proposed method is its independence from any mesh of the computing domain, along with its straightforward implementation and  high numerical stability. To ensure the efficiency of the presented method, we have investigated the convergence of  the proposed method.  The  obtained numerical results confirm the theoretical achievements and demonstrate the method's effectiveness and accuracy. https://jmm.guilan.ac.ir/article_8877_0e8645523f08c816df68dccfae64f1ba.pdf