LAUSR

Within the framework of edge-based smoothed point interpolation method (ES-PIM), a fully automatic adaptive procedure has been proposed by introducing a novel local critical value definition. Owing to the softened stiffness, ES-PIM can generally provide much better results than the traditional finite element method using the simplest linear triangle elements. By comparing with most adaptive models which need to set a refinement rate manually, a novel local critical value considering the area-dependent average magnitude of error indicator for all the cells has been introduced in this work, which leads to an adaptive ES-PIM model without manual operation during the adaptive process. Numerical results have shown that the present adaptive model conducts the adaptive process dynamically, adds the new nodes properly and provides more accurate results with less field nodes than both the model with uniform refinement and the adaptive model using predefined refinement rate. Also considering linear triangular background elements used, the present method is supposed to have much potential for solving complicated engineering problems.