Adaptive meshless refinement schemes for RBF-PUM collocation
This work addresses the need for adaptive refinement in meshless methods for PDEs, offering a tailored strategy for RBF-PUM collocation.
The paper presents an adaptive discretization technique for solving elliptic PDEs using a collocation RBF-PUM method, proposing a new error indicator and refinement algorithm. Numerical tests demonstrate the effectiveness of the adaptive scheme.
In this paper we present an adaptive discretization technique for solving elliptic partial differential equations via a collocation radial basis function partition of unity method. In particular, we propose a new adaptive scheme based on the construction of an error indicator and a refinement algorithm, which used together turn out to be ad-hoc strategies within this framework. The performance of the adaptive meshless refinement scheme is assessed by numerical tests.