Multiscale methods with compactly supported radial basis functions for the Stokes problem on bounded domains
This work addresses the need for efficient numerical methods for the Stokes problem, but the results are incremental as they extend existing RBF techniques to a specific PDE system.
The paper develops a multiscale collocation method using compactly supported radial basis functions for the Stokes problem, providing convergence and stability analysis with numerical validation.
In this paper, we investigate the application of radial basis functions (RBFs) for the approximation with collocation of the Stokes problem. The approximate solution is constructed in a multi-level fashion, each level using compactly supported radial basis functions with decreasing scaling factors. We use symmetric collocation and give sufficient conditions for convergence and stability analysis is also presented. Numerical experiments support the theoretical results.