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Existence and stability, and discrete BB and rank conditions, for general mixed-hybrid finite elements in elasticity. (English) Zbl 0624.73094

Hybrid and mixed finite element methods, Winter Annu. Meet. ASME, Miami Beach/Fl. 1985, AMD-Vols. 73, 91-112 (1985).
[For the entire collection see Zbl 0623.00027.]
In this paper, all possible forms of mixed-hybrid finite element methods that are based on multi-field variational principles are examined as to the conditions for existence, stability, and uniqueness of their solutions. The reasons as to why certain “simplified hybrid-mixed methods” in general, and the so-called “simplified hybrid-displacement method” in particular (based on the so-called simplified variational principles), become unstable, are discussed. A comprehensive discussion of the “discrete” BB-conditions, and the rank conditions, of the matrices arising in mixed-hybrid methods, is given. Some recent studies aimed in the assurance of such rank conditions, and the related problem of the avoidance of spurious kinematic modes, are presented.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
65K10 Numerical optimization and variational techniques

Citations:

Zbl 0623.00027