Macro-Hybrid Variational Formulations of Constrained Boundary Value Problems |
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Authors: | Gonzalo Alduncin |
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Affiliation: | 1. Institute of Geophysics , National Autonomous University of Mexico , Coyoacan, Mexico alduncin@geofisica.unam.mx |
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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. |
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Keywords: | Augmented variational formulations Composition duality methods Constrained boundary value problem Hybrid domain decomposition Proximal-point algorithms Subdifferential equations |
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