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This paper studies the stability of velocity-pressure mixed approximations ofthe Stokes problem when different finite element (FE) spaces for each componentof the velocity field are considered. We consider some new combinations ofcontinuous FE reducing the number of degrees of freedom in some velocitycomponents. Although the resulting FE combinations are not stable in general,by using the Stenberg's macro-element technique, we show their stability in awide family of meshes (namely, in uniformly unstructured meshes). Moreover, apost-processing is given in order to convert any mesh family in an uniformlyunstructured mesh family. Finally, some 2D and 3D numerical simulations areprovided agree with the previous analysis.

On the stability of approximations for the Stokes problem using different finite element spaces for each component of the velocity