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

1432-0924

Springer Online Journal Archives 1860-2000

Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Summary In this paper the general hybrid-mixed finite element methods are investigated systematically in a framework of multi-field 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 BB-conditions. 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 finite element methods.

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