Hokkaido Mathematical Journal

NAKAO Mitsuhiro T., HASHIMOTO Kouji, KOBAYASHI Kenta,

Verified numerical computation of solutions for the stationary Navier-Stokes equation in nonconvex polygonal domains.

Hokkaido Mathematical Journal, 36 (2007) pp.777-799

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Abstract

We propose a method to enclose solutions for the stationary Navier-Stokes equation in nonconvex polygonal domains. Our method is based on an infinite dimensional Newton-type formulation by using the finite element method with constructive error estimates and fixed point theorems. Numerical examples related to the step flow problems in $L$-shape domain are presented.

MSC(Primary)35J60
MSC(Secondary)65N15
Uncontrolled KeywordsNavier-Stokes equation, nonconvex polygonal domains, step flow