Inf-Sup Conditions for twofold saddle point problems

Many problems in continuous fluid and solid mechanics lead to variational problems with a saddle point structure. In this talk we discuss necessary and sufficient conditions for existence and uniqueness of solutions for these problems. This work extends the classical saddle point theory to accommodate nonlinear constitutive relations and the twofold saddle structure. An application to problems in incompressible fluid mechanics employing symmetric tensor finite elements for the stress approximation is presented.