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In this paper, we first construct a nonconforming finite element pair for theincompressible Stokes problem on quadrilateral grids, and then construct adiscrete Stokes complex associated with that finite element pair. The finiteelement spaces involved consist of piecewise polynomials only, and thedivergence-free condition is imposed in a primal formulation. Combined withsome existing results, these constructions can be generated onto grids thatconsist of both triangular and quadrilateral cells.

Stable finite element pair for Stokes problem and discrete Stokes complex on quadrilateral grids