Composition duality methods for evolution mixed variational inclusions

Composition duality methods are presented for the qualitative and discretization analysis of primal and dual evolution mixed variational inclusions in reflexive Banach spaces. Abstract applications to macro-hybrid variational formulations, semi-discrete internal approximations globally nonconforming and time marching schemes implementable as multidomain proximal-point algorithms are studied. Stationary fully discrete inclusions are considered as well as corresponding preconditioned penalty–duality algorithms. To illustrate the theory, a monotone distributed control diffusion problem is treated.