Adaptive meshless refinement schemes for RBF-PUM collocation (Q1726598)

The paper is about an adaptive refinement strategy for RBF approximation of elliptic PDEs. The idea consists of a new error indicator and a new strategy to add or remove collocation points. The error indicator is of residual type. In each iteration, a solution is obtained by the current set of collocation points. Then a set of test collocation points are used to evaluate the residual, and these points are added to the set of trial collocation points if the residual is larger then a certain tolerance, and are removed if the residual is small enough. Some numerical examples are used to test the performance.