A Family of Multiscale Hybrid Mixed Finite Element Methods for the Darcy Equation with Rough Coefficients

Paredes, D; Harder, C; Valentin F.

Abstract

We aim at proposing novel stable finite element methods for the mixed Darcy equation with heterogeneous coefficients within a space splitting framework. We start from the primal hybrid formulation of the elliptic model for the pressure. Localization of this infinite-dimensional problem leads to element-level boundary value problems which embed multiscale and high-contrast features in a natural way, with Neumann boundary conditions driven by the Lagrange multipliers. Such a procedure leads to methods involving the space of piecewise constants for the pressure together with a discretization of the fluxes. Choosing (arbitrarily) polynomial interpolations, the lowest-order Raviart-Thomas element as well as some recent multiscale methods are recovered. In addition, the methods assure local mass conservation and can be interpreted as stabilized primal hybrid methods. Extensive numerical validation attests to the accuracy of the new methods on academic and more realistic problems with rough coefficients. © 2013 Elsevier Inc.

Más información

Título según SCOPUS: A family of Multiscale Hybrid-Mixed finite element methods for the Darcy equation with rough coefficients
Título de la Revista: JOURNAL OF COMPUTATIONAL PHYSICS
Volumen: 245
Editorial: ACADEMIC PRESS INC ELSEVIER SCIENCE
Fecha de publicación: 2013
Página de inicio: 107
Página final: 130
Idioma: English
DOI:

10.1016/j.jcp.2013.03.019

Notas: SCOPUS - ISI