Abstract multiscale-hybrid-mixed methods

Resumo

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.

Ficha do documento

Tipo

Artigo científico

Ano

2015

Instituição

Springer-Verlag Italia Srl

Fonte

Repositório da FGV

Idioma

Inglês

Acesso

Acesso restrito

DOI

10.1007/s10092-014-0129-5

Identificador

oai:repositorio.fgv.br:10438/23516

Temas

Dados

Palavras-chave

MHMMixed methodHybrid methodDomain decompositionFinite elementMultiscaleMatemáticaEscala finita (Fisica estatistica)