Macro-hybrid variational formulations of constrained boundary value problems

作者：Alduncin Gonzalo^*

来源：Numerical Functional Analysis and Optimization, 2007, 28(7-8): 751-774.

DOI：10.1080/01630560701493206

• augmented variational formulations
• composition duality methods
• constrained boundary value problem
• hybrid domain decomposition
• proximal-point algorithms
• subdifferential equations

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.

• 出版日期2007