An Adaptive LOOCV-Based Algorithm for Solving Elliptic PDEs via RBF Collocation

摘要

We present a new adaptive scheme for solving elliptic partial differential equations (PDEs) through a radial basis function (RBF) collocation method. Our adaptive algorithm is meshless and it is characterized by the use of an error indicator, which depends on a leave-one-out cross validation (LOOCV) technique. This approach allows us to locate the areas that need to be refined, also including the chance to add or remove adaptively any points. The algorithm turns out to be flexible and effective by means of a good interaction between error indicator and refinement procedure. Numerical experiments point out the performance of our scheme.