Application of lRBF-FD method for Numerical solutionof the obstacle problem

The obstacle problem is a nonlinear variational inequality, first introduced to model contact phenomena in solid mechanics. Because of the singularity of the solution along the free boundary, the development of accurate and efficient numerical methods is critical. This paper introduces a novel meshless technique for numerically solving the obstacle problem, utilizing the local radial basis function-finite difference (lRBF-FD) method. An active set strategy is combined with the lRBF-FD method to manage the complementarity condition of the problem. Notable advantages of this method are its independence from any mesh and its straightforward implementation with high numerical stability.