Abstract
Conforming finite element pairs for the three-dimensional Stokes problem on general simplicial triangulations are constructed. The pressure space simply consists of piecewise constants, where as the velocity space consists of cubic polynomials augmented with rational functions. We show the existence of a bounded Fortin projection and therefore the necessary LBB condition is satisfied. In addition the divergence operator maps the velocity space into the space of piecewise constants. Consequently, the method produces exactly divergence-free velocity approximations.
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