A Mixed Finite Element Method for the Stokes Equations Based on a Weakly Over-Penalized Symmetric Interior Penalty Approach

Authors:
Andrew T. Barker;Susanne C. Brenner
Affiliations:
Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, USA 70803-4918 and Max Planck Institute for Dynamics of Complex Technical Systems, Mag ...;Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, USA 70803-4918
Venue:
Journal of Scientific Computing
Year:
2014

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Abstract

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 $$L_2$$L2 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.