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

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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 \(L_2\) 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.

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Author notes

  1. Andrew T. Barker

    Present address: Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 , Magdeburg, Germany

Authors and Affiliations

  1. Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana, 70803-4918, USA

    Andrew T. Barker & Susanne C. Brenner

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  1. Andrew T. Barker
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  2. Susanne C. Brenner
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Correspondence to Susanne C. Brenner.

Additional information

The work of the first author was supported in part by the National Science Foundation VIGRE Grant DMS-07-39382. The work of the second author was supported in part by the National Science Foundation under Grant No. DMS-10-16332.

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Barker, A.T., Brenner, S.C. A Mixed Finite Element Method for the Stokes Equations Based on a Weakly Over-Penalized Symmetric Interior Penalty Approach. J Sci Comput 58, 290–307 (2014). https://doi.org/10.1007/s10915-013-9733-9

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  • DOI: https://doi.org/10.1007/s10915-013-9733-9

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