Navier-Stokes方程简单分歧点的谱Galerkin逼近

Spectral Galerkin Approximation of Simple Bifurcation Point of the Navier-Stokes Equations

针对分歧难以数值计算的问题 ,通过分析Navier Stokes方程简单分歧点的性质 ,构造出定常Navier Stokes方程非退化简单分歧点的扩充系统及其谱Galerkin逼近扩充系统 ,证明了谱Galerkin逼近扩充系统解的存在性和收敛性 .运用Stokes算子的特征值 ,给出了谱逼近的误差估计 .由于所构造的扩充系统的导数具有分块下三角形式 ,采用分块迭代的方法进行数值求解 ,不仅减少了计算量 ,而且是二次收敛的 ,从而为Navier

Spectral Galerkin approximation problem of bifurcation point of the NavierStokes equations is studied. By analyzing property of simple bifurcation point, the extended system and its spectral Galerkin approximation extended system of nondegenerate simple bifurcation point of the NavierStokes equations are constructed. The existence and convergence of solutions of the approximation extended system are proved, moreover, the error estimations of spectral approximation are given by using eigenvalue of Stokes operator. Because the derivation of the extended system has a block lower triangular form, the method of splitting iteration is applied to compute simple bifurcation point, not only computational work is reduced, but also local quadratic convergence is achieved. Accordingly, the valid algorithm for nondegenerate simple bifurcation point of the NavierStokes equations is given.