For the stationary Navier-Stokes system of incompressible or compressible flows on polygonal domains and numerical simulations

Abstract

In this dissertation, we study existence and regularity results of the solution for the stationary Navier-Stokes system of incompressible or compressible flows with no-slip boundary condition on polygonal domains. First, we describe the corner singularity theory for the Stokes system, and derive the regularity results based on this theory of the solution for our problems. In addition, a finite element method describing the singular behavior at corner of solutions to the stationary Navier-Stokes system of incompressible flows is investigated on a non-convex polygon. We construct finite element approximations for the stress intensity factors and the regular part, show unique existence of the approximations, and derive the error estimates. Some numerical examples are given, confirming the error estimates.