Analytical solution of Stokes flow near corners and applications to numerical solution of Navier-Stokes equations with high precision. (English) Zbl 1313.76035

Burda, Pavel; Novotný, Jaroslav; Šístek, Jakub

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, May 2–5, 2012. In honor of the 60th birthday of Michal Křížek. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-60-8/pbk). 43-54 (2012).

Summary: We present analytical solution of the Stokes problem in 2D domains. This is then used to find the asymptotic behavior of the solution in the vicinity of corners, also for Navier-Stokes equations in 2D. We apply this to construct very precise numerical finite element solution.
For the entire collection see [Zbl 1277.00031].

MSC:

76D06	Statistical solutions of Navier-Stokes and related equations
76D05	Navier-Stokes equations for incompressible viscous fluids
76M10	Finite element methods applied to problems in fluid mechanics
35Q30	Navier-Stokes equations

Keywords:

Navier-Stokes equations; corner singularities; finite element method; numerical results