A numerical method for solving the Oseen-type problem in an $L$-shaped domain

In this paper we introduce the notion of an $R_{\nu}$-generalized solution to the Oseen-type problem in rotation form in a polygonal domain with a reentrant obtuse angle on its boundary. We propose a weighted finite element method to solve this problem approximately. A number of numerical experiments performed on a model problem in an $L$-shaped domain show the advantages of the proposed method.