4 research outputs found
Comparison results for the Stokes equations
This paper enfolds a medius analysis for the Stokes equations and compares
different finite element methods (FEMs). A first result is a best approximation
result for a P1 non-conforming FEM. The main comparison result is that the
error of the P2-P0-FEM is a lower bound to the error of the Bernardi-Raugel (or
reduced P2-P0) FEM, which is a lower bound to the error of the P1
non-conforming FEM, and this is a lower bound to the error of the MINI-FEM. The
paper discusses the converse direction, as well as other methods such as the
discontinuous Galerkin and pseudostress FEMs.
Furthermore this paper provides counterexamples for equivalent convergence
when different pressure approximations are considered. The mathematical
arguments are various conforming companions as well as the discrete inf-sup
condition
A mixed finite element method for the stokes equations based on a weakly over-penalized symmetric interior penalty approach
We present a mixed finite element method for the steady-state Stokes equations where the discrete bilinear form for the velocity is obtained by a weakly over-penalized symmetric interior penalty approach. We show that this mixed finite element method is inf-sup stable and has optimal convergence rates in both the energy norm and the L 2 norm on meshes that can contain hanging nodes. We present numerical experiments illustrating these results, explore a very simple adaptive algorithm that uses meshes with hanging nodes, and introduce a simple but scalable parallel solver for the method. © 2013 Springer Science+Business Media New York