Domain decomposition method and numerical analysis of a fluid dynamics problem

• Published in: Computational mathematics and mathematical physics Vol. 54; no. 9; pp. 1459 - 1480
• Main Author: Rukavishnikov, A. V.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-09-2014; Springer Nature B.V
• Subjects: Applied mathematics; Boundaries; Computational fluid dynamics; Computational mathematics; Computational Mathematics and Numerical Analysis; Decomposition; Discretization; Finite element analysis; Fluid dynamics; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; Navier-Stokes equations; Norms; Numerical analysis; Studies; domain decomposition method; incompressible Navier-Stokes equations; estimate of the convergence rate of the discrete solution to the exact one; mortar elements; nonconforming finite element method
• ISSN: 0965-5425; 1555-6662
• DOI: 10.1134/S0965542514070094

A two-dimensional problem obtained by time discretization and linearization of a viscous flow governed by the incompressible Navier-Stokes equations is considered. The original domain is divided into subdomains such that their interface is a smooth (nonclosed, self-avoiding) curve with the ends belonging to the boundary of the domain. A nonconforming finite element method is constructed for the problem, and the convergence rate of the discrete solution of the problem to the exact one is estimated in the
L
2
(Ω
h
) norm.