Theoretical analysis and construction of numerical method for solving the Navier–Stokes equations in rotation form with corner singularity

Abstract

In this paper, we introduced the notion of an Rν-generalized solution of the Oseen problem in rotation form in two-dimensional polygonal domain with a reentrant corner at the boundary. Its existence and uniqueness in the nonsymmetric variational formulation of the problem is established. An estimate related to the conservation of the energy balance of the approximation velocity field for the Navier–Stokes problem in the rotation form is obtained. A weighted finite element method is constructed. A series of numerical experiments of test examples based on the proposed method is carried out. A comparative analysis of the approach with the classical FEM is performed. The results of numerical experiments showed a significant advantage of the proposed approach.