How to Choose Basis Functions in Meshless Methods?
Technical progress in construction of computers, their higher speed, and larger memory gave possibility to develop new numerical methods for solution of boundary value problems. A lot of meshless methods have been developed in last years. Some of them are in a way identical with the Galerkin method, where the trial space is formed by especially constructed functions. The choice of the proper trial space is important, because the error in the Galerkin method is determined by the fact how well the exact solution can be approximated by the elements from this finite dimensional space.
In this contribution different trial spaces are considered. We will construct spaces generated by means of B-splines and shape functions received by means of the RKP technique. Examples of using trial spaces mentioned for solution of some boundary value problems will be given. We focus our attention on error estimates in these cases too.
KeywordsMeshless methods Galerkin method B-spline basis RKP shape function basis
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