Mathematical aspects of the general hybrid-mixed finite element methods and singular-value principle

In this paper the general hybrid-mixed ®nite element methods are investigated systematically in a framework of multi-®eld variational equations. The commonly accepted concept ``saddle point problem'' is argued in this paper. The existence, uniqueness, convergence, and stability properties of the solutions are proved undertaking the assumptions of Ker*-ellipticity and nested BBconditions. The relation between discrete BB-condition and smallest singular value, and a so-called singular value principle are proposed for the practical applications using hybrid-mixed ®nite element methods.