Weighted finite element method for the Stokes problem with corner singularity

In this paper we introduce the notion of Rν-generalized solution to the Stokes problem with singularity in a non-convex polygonal domain with one reentrant corner of 3π2 on its boundary. The weighted analogue of the Ladyzhenskaya-Babus̆ka-Brezzi condition is proved. A new weighted finite element method is constructed. Results of numerical experiments have shown the efficiency of the method.