Macro-Hybrid Variational Formulations of Constrained Boundary Value Problems

Abstract

In the context of convex analysis, macro-hybrid variational formulations of constrained boundary value problems are presented. Monotone mixed variational inclusions are macro-hybridized on the basis of nonoverlapping domain decompositions, and corresponding three-field versions are derived. Then, for regularization purposes, augmented formulations are established via preconditioned exact penalizations and expressed in terms of proximation operators. Optimization interpretations are given for potential problems, recovering the classic two- and three-field augmented Lagrangian formulations. Furthermore, associated parallel two- and three-field proximal-point algorithms are discussed for numerical resolution of finite element discretizations. Applications to dual mixed variational formulations of problems from mechanics illustrate the theory.

Keywords:

• Augmented variational formulations
• Composition duality methods
• Constrained boundary value problem
• Hybrid domain decomposition
• Proximal-point algorithms
• Subdifferential equations

AMS Subject Classification:

• 35A15
• 47H05
• 35J50
• 35J85
• 49J53

ACKNOWLEDGMENT

This research has been partially supported by the Program on Naturally Fractured Reservoirs of the Mexican Institute of Petroleum, IMP.