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Calcolo

, Volume 52, Issue 4, pp 543–557 | Cite as

Abstract multiscale-hybrid-mixed methods

  • Alexandre L. MadureiraEmail author
Article

Abstract

In an abstract setting, we investigate the basic ideas behind the Multiscale Hybrid Mixed (MHM) method, a Domain Decomposition scheme designed to solve multiscale partial differential equations (PDEs) in parallel. As originally proposed, the MHM method starting point is a primal hybrid formulation, which is then manipulated to result in an efficient method that is based on local independent PDEs and a global problem that is posed on the skeleton of the finite element mesh. Recasting the MHM method in a more general framework, we investigate some conditions that yield a well-posed method. We apply the general ideas to different formulations, and, in particular, come up with an interesting and fruitful connection between the Multiscale Finite Element Method and a dual hybrid method. Finally, we propose a method that combines the main ideas of the Discontinuous Enrichment Method and the MHM method.

Keywords

MHM Mixed method Hybrid method Domain decomposition Finite element Multiscale 

Mathematics Subject Classification

65N12 65N30 

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Copyright information

© Springer-Verlag Italia 2014

Authors and Affiliations

  1. 1.Laboratório Nacional de Computação CientíficaPetrópolis-RJBrazil
  2. 2.Fundação getúlio vargasRio de Janeiro-RJBrazil

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