We consider higher order mixed finite element methods for the incompressible Stokes or Navier-Stokes equations with -elements for the velocity and discontinuous -elements for the pressure where the order can vary from element to element between and a fixed bound . We prove the inf-sup condition uniformly with respect to the meshwidth on general quadrilateral and hexahedral meshes with hanging nodes.
In the second part of the paper, we compare the solutions produced in the framework of the conference “Mathematical and numerical aspects of low Mach number flows” organized by INRIA and MAB in Porquerolles, June 2004, to the reference solutions described in Part 1. We make some recommendations on how to produce good quality solutions, and list a number of pitfalls to be avoided.
In the second part of the paper, we compare the solutions produced in the framework of the conference “Mathematical and numerical aspects of low Mach number flows” organized by INRIA and MAB in Porquerolles, June 2004, to the reference solutions described in Part 1. We make some recommendations on how to produce good quality solutions, and list a number of pitfalls to be avoided.
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