Inf–sup conditions for twofold saddle point problems

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...

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Bibliographic Details
Published in:Numerische Mathematik 2011-08, Vol.118 (4), p.663-693
Main Authors: Howell, Jason S., Walkington, Noel J.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical analysis. Scientific computation
Numerical and Computational Physics
Sciences and techniques of general use
Simulation
Theoretical
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Summary: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.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-011-0372-5