Abstract: In this paper, we propose an adaptive mesh method based on the radial basis function. The proposed method uses the information of the numerical solution provided by the mesh dependence method and the difference solution from the radial basis function to refine or coarse the mesh. Our method takes full advantage of the simple format and the flexible node configuration that the radial basis function possessed and the robustness of the mesh-depended method. The proposed algorithm is easy to implement. The numerical examples show that the proposed algorithm can refine the mesh in the region where the solution changes dramatically and coarsen the mesh in the region where the solution changes gradually. Therefore, it can save an enormous amount of calculating time while ensuring the same numerical accuracy.

Key words: radial basis function, finite element method, adaptive mesh method, partial differential equation