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

Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality九州大学21世紀COEプログラム「機能数理学の構築と展開」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