Augmented Macro-Hybrid Mixed Finite Element Schemes for Elastic Contact Problems

Abstract

On a setting of subdifferential models, variational augmented macro-hybrid mixed finite element schemes are formulated and analyzed for elastic unilateral contact problems with prescribed friction. Composition duality principles determine primal and dual mixed solvability, adopting coupling surjectivity for dualization. Macro-hybridization corresponds to nonoverlapping decompositions of elastic solid body systems, with displacement continuity and traction equilibrium transmission conditions dualized. In general, traction and displacement multipliers synchronize sub-bodies through nonmatching finite element interfaces. Three-field formulations give the basis for variational augmentation, in a sense of exact penalization, allowing speed-up of rates of convergence as well as proximation procedures of parallel numerical resolution algorithms.