Adaptive Analysis with Mesh-free Method using the Double Projection method (2) -Adaptive Refinement-

The adaptive analysis and refinement of mesh-free method based on improved error estimating scheme called “double projection method” were presented. This is succeeding study of our previous paper on double projection method for reducing the spurious oscillation of error distribution. In this paper, a new algorithm for adaptive refinement which makes an advantage of smoothed distribution of error from double projection method were proposed. Since the distribution of double projected error is very similar to real one, there would be no need of iterative analysis, error estimation and refinement in adaptive process; the process of error estimation and refinement is performed for one time and refinement can be iterated several times. To present the efficiency of proposed adaptive refinement using double projected error, the numerical experiments were performed to several linear two-dimensional problems. The results showed remarkable improvement of convergence ratios compare to those of previous projection method. Moreover, if the more precise refinement scheme is adopted, the better result could be obtained.