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Inf–sup conditions for twofold saddle point problems

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Abstract

Necessary and sufficient conditions for existence and uniqueness of solutions are developed for twofold saddle point problems which arise in mixed formulations of problems in continuum mechanics. This work extends the classical saddle point theory to accommodate nonlinear constitutive relations and the twofold saddle structure. Application to problems in incompressible fluid mechanics employing symmetric tensor finite elements for the stress approximation is presented.

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Authors and Affiliations

  1. Department of Mathematics, Clarkson University, Potsdam, NY, 13676, USA

    Jason S. Howell

  2. Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Noel J. Walkington

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  1. Jason S. Howell
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  2. Noel J. Walkington
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Correspondence to Jason S. Howell.

Additional information

J. S. Howell: This material is based in part upon work supported by the Center for Nonlinear Analysis (CNA) under the National Science Foundation Grant No. DMS-0635983. N. J. Walkington: Supported in part by National Science Foundation Grants DMS-0811029. This work was also supported by the NSF through the Center for Nonlinear Analysis.

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Howell, J.S., Walkington, N.J. Inf–sup conditions for twofold saddle point problems. Numer. Math. 118, 663–693 (2011). https://doi.org/10.1007/s00211-011-0372-5

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  • DOI: https://doi.org/10.1007/s00211-011-0372-5

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