A multiscale mortar multipoint flux mixed finite element method

In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finit...

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Bibliographic Details
Published in:ESAIM. Mathematical modelling and numerical analysis 2012-07, Vol.46 (4), p.759-796
Main Authors: Wheeler, Mary Fanett, Xue, Guangri, Yotov, Ivan
Format: Article
Language:English
Subjects:
65N06
65N12
65N15
65N22
65N30
76S05
Algebra
Approximation
cell-centered finite difference
Convergence
Decomposition
Exact sciences and technology
Finite element analysis
Finite element method
Flexibility
Flux
full tensor coefficient
hexahedra
Interfaces
Mathematical analysis
Mathematical models
Mathematics
Methods
mixed finite element
mortar finite element
Mortars
multiblock
multipoint flux approximation
Multiscale
nonmatching grids
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Permeability
Polynomials
quadrilaterals
Sciences and techniques of general use
Studies
Velocity
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Summary:In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method.
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2011064