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

作者：Barker Andrew T; Brenner Susanne C^*

来源：Journal of Scientific Computing, 2014, 58(2): 290-307.

DOI：10.1007/s10915-013-9733-9

• Stokes problem
• Mixed finite element method
• Discontinuous finite element method
• Weakly over-penalized symmetric interior penalty method
• Nonconforming meshes
• Adaptive algorithm
• Additive Schwarz preconditioners

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 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.

• 出版日期2014-2