The C¹ wavelet method for numerical solutions of the Neumann problem

Abstract

In this article we use the C ¹ wavelet bases on Powell-Sabin triangulations to approximate the solution of the Neumann problem for partial differential equations. The C ¹ wavelet bases are stable and have explicit expressions on a three-direction mesh. Consequently, we can approximate the solution of the Neumann problem accurately and stably. The convergence and error estimates of the numerical solutions are given. The computational results of a numerical example show that our wavelet method is well suitable to the Neumann boundary problem.

Keywords:

• C ¹ spline wavelet
• Powell–Sabin elements
• Neumann problem

AMS Subject Classifications: :

• 65N30
• 65T60

Acknowledgements

This work is supported in part by NSF of Hainan under grant 80525, the “515” Scientists program of Hainan province and the professorial fund of Hainan normal university. These supports are gratefully acknowledged.