Least-squares RBF-FD method for the incompressible Stokes equations with the singular source

Abstract

In this article, we propose the least-squares RBF-FD method for the incompressible Stokes equations with the singular source along the interface. First, we apply Green’s formula to derive interface conditions, then by employing the RBF-FD method to directly discretize the spatial operators, a least-squares system about the incompressible Stokes equations with interface conditions is constructed. The discrete least-squares system is derived by introducing the weight coefficient. We obtain the error bound of discrete least-squares system using the RBF interpolant theorem. Some numerical examples are provided to show the convergency and efficiency of the least-squares RBF-FD method for the incompressible Stokes equations with the singular source.

Acknowledgments

The authors would like to thank the editor and referees for their valuable comments and suggestions which helped us to improve the results of this paper.

Additional information

Funding

This work is in parts supported by the NSF of Xinjiang Province (No. 2016D01C058), the Research Fund from Key Laboratory of Xinjiang Province (No. 2017D04030), the Xinjiang Provincial University Research Foundation of China (No. XJEDU2018I002), and the NSF of China (No. 11671345).