Weighted finite element method for the Stokes problem with corner singularity

Abstract In this paper we introduce the notion of R ν -generalized solution to the Stokes problem with singularity in a non-convex polygonal domain with one reentrant corner of 3 π 2 on its boundary. The weighted analogue of the Ladyzhenskaya–Babuska–Brezzi condition is proved. A new weighted finite element method is constructed. Results of numerical experiments have shown the efficiency of the method.

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