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We consider residual-based stabilised finite element methods for the generalised Oseen problem. The unique solvability based on a modified stability condition and an error estimate are proved for inf-sup stable discretisations of velocity and pressure. The analysis highlights the role of an additional stabilisation of the incompressibility constraint. It turns out that the stabilisation terms of the streamline-diffusion (SUPG) type play a less important role. In particular, there exists a conditional stability problem of the SUPG stabilisation if two relevant problem parameters tend to zero. The analysis extends a recent result to general shape-regular meshes and to discontinuous pressure interpolation. Some numerical observations support the theoretical results.

Dedicated to Raytcho Lazarov on the occasion of his 60th birthday.Abstract -A boundary-value problem with a nonlocal integral condition is considered for a two-dimensional elliptic equation with constant coefficients and a mixed derivative. The existence and uniqueness of a weak solution of this problem are proved in a weighted Sobolev space. A difference scheme is constructed using the Steklov averaging operators. It is proved that the difference scheme converges in discrete W

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