The convergence of the spectral scheme for solving two-dimensional vorticity equations. (English) Zbl 0599.76030

Guo, Benyu

J. Comput. Math. 1, 353-362 (1983).

The author proposed a technique to prove the strict error estimation of the spectral scheme for the KdV-Burgers equation [Acta Math. Sin. 28, 1- 15 (1985; Zbl 0574.65135)]. In this paper, the technique is generalized to two-dimensional vorticity equations. Under some conditions, the error estimation implies the convergence. The more smooth the solution of the vorticity equations, the more accurate the approximate solution.

MSC:

76B47	Vortex flows for incompressible inviscid fluids
35Q99	Partial differential equations of mathematical physics and other areas of application

Keywords:

Korteweg-de Vries-Burgers equation; strict error estimation; spectral scheme; two-dimensional vorticity equations; convergence; approximate solution

Citations:

Zbl 0574.65135