Composition Duality Methods for Mixed Variational Inclusions

Analysis of augmented three-field macro-hybrid mixed finite element schemes

“…Following the preconditioned augmented variational method studied in [2], but in the context of linear mixed variational problems, let r > 0 be a fixed exact penalization parameter, and let…”

“…, ∀ζ * e ∈ B * (Γ e ), e = 1, 2, ··· , E. Thereby, according to [4] (see also [2]), for operators and functions of local type with respect to decompositions (5) …”

“…We shall follow our previous work [2] on composition duality methods for mixed variational inclusions or inequalities.…”

“…In the next two sections, we shall determine a priori error estimates as well as rates of convergence of finite element implementations. Following [2], our strategy will be to develop three-field macro-hybrid mixed discretizations as three-field versions of macro-hybrid mixed discrete problems.…”

Evolution Mixed Variational Inclusions with Optimal Control

“…We should note that for a fully dual compositional duality principle in the sense of (Alduncin, G., 2005a(Alduncin, G., , 2005b, the surjectivity of the total small strain transpose operator −H T ∈ L(Y(Ω), V * (Ω)) would be required, guaranteeing the sufficiency of compositional dualization (32) and, consequently, the sufficiency of the above dual duality principle. However, such a total small strain transpose operator surjectivity would require of a primal quotient space V(Ω) setting (Girault, V. & Raviart, P.-A., 1986).…”