New numerical approach for solving the oseen problem in a convection form in non-convex domain

摘要

In the paper, we consider stationary, linearized by Picard's iterations, Navier-Stokes equations governing the flow of a incompressible viscous fluid in the convection form in non-convex polygonal domain. An R_v-generalized solution of the problem is defined. A weighted finite element method for finding an approximate R_v-generalized solution is constructed. Numerically shown that the convergence rate does not depend on a value of the reentrant corner in the norm of the weighted Sobolev space.