Wavelet Natural Boundary Element Method for the Neumann Exterior Problem of Stokes Equations

Natural boundary element approach is a promising method to solve boundary value problems of partial differential equations. This paper addresses the Neumann exterior problem of Stokes equations using the wavelet natural boundary element method. The Stokes exterior problem is reduced into an equivalent Hadamard-singular Natural Integral Equation (NIE). By virtue of the wavelet-Galerkin algorithm, the simple and accurate computational formulae of stiffness matrix are obtained. The 2J+3 × 2J+3 stiffness matrix is sparse and determined only by its 2J + 3J + 1 entries. It greatly decreases the computational complexity. Also, the condition number of stiffness matrix is , where N is the discrete node number. This indicates that the proposed algorithm is more stable than that of classical finite element method. The error estimates are established for the wavelet-Galerkin approximate solution. Several numerical examples are given to evaluate the performance of our method with encouraging results.