Adaptive Meshfree Method Based on Local Thin Plate Spline Radial Basis Interpolation for the Solution of High Gradient Problems

An adaptive meshfree method based on local thin-plate spline radial basis interpolation and collocation schemes was applied to solve partial differential equations (PDEs) with high gradient. Special attention was paid to the detection of high gradient regions, and the adjustment coefficient is adopted to gain these nodes which need to be refined. The numerical results demonstrate that a good improvement of approximate accuracy can be obtained after using adaptive node refinement in high gradients.