A study of axisymmetric Stokes flows using a Hybrid-Mixed Finite Element formulation

Resumo

We propose a hybrid-mixed finite element formulation based on H(div)-conforming velocity and discontinuous pressure approximations for axisymmetric Stokes flows. This scheme is locally conservative, which means that mass conservation is strongly satisfied at element level resulting in exact divergence-free solutions for incompressible flows. The normal component continuity of vector quantities over the element interfaces is automatically guaranteed, while the tangential conformity is weakly imposed by a traction that acts as a Lagrange multiplier. For stability purposes, there must be a compatibility between the approximation spaces used for velocity and traction that fulfills the inf-sup condition. The developed numerical method is verified against classical bench-
marks that have analytical solutions available in the literature, and its convergence properties are also investigated in different scenarios. The resulting code is implemented in an open source C++ object-oriented computational environment called NeoPZ.