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The recent developed method, radial basis function based finite element method (RBF-FEM) could solve the partial differential equation engineering problems. The RBF-FEM method utilizes the radial basis functions to generate the shape functions from the node in the element (the nonoverlapping region). When the problems in terms of localized deformation, or steep gradients, or even discontinuity regions are posed, a fine mesh is created to produce more accurate results. Therefore a mesh refinement technique is employed in order to reduce the computational time cost. This study introduces an extension of the RBF-FEM on quadtree mesh.
The proposed approach combines RBF-FEM and the polygonal finite element method, which is the so-called RBF-PolyFEM, to construct conforming approximations on quadtree mesh refinement. Numerical examples are presented to demonstrate the accuracy and performance of the proposed h-adaptive RBF-FEM approach in comparison to other numerical methods.

numerical methods; interpolation; computation; simulation