Displaying similar documents to “Multiplicative Schwarz Methods for Discontinuous Galerkin Approximations of Elliptic Problems”

Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: non-overlapping case

Paola F. Antonietti, Blanca Ayuso (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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We propose and study some new additive, two-level non-overlapping Schwarz preconditioners for the solution of the algebraic linear systems arising from a wide class of discontinuous Galerkin approximations of elliptic problems that have been proposed up to now. In particular, two-level methods for both symmetric and non-symmetric schemes are introduced and some interesting features, which have no analog in the conforming case, are discussed. Both the construction and analysis of the...

Analysis of two-level domain decomposition preconditioners based on aggregation

Marzio Sala (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this paper we present two-level overlapping domain decomposition preconditioners for the finite-element discretisation of elliptic problems in two and three dimensions. The computational domain is partitioned into overlapping subdomains, and a coarse space correction is added. We present an algebraic way to define the coarse space, based on the concept of aggregation. This employs a (smoothed) aggregation technique and does not require the introduction of a coarse grid. We consider...

Multiscale finite element coarse spaces for the application to linear elasticity

Marco Buck, Oleg Iliev, Heiko Andrä (2013)

Open Mathematics

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We extend the multiscale finite element method (MsFEM) as formulated by Hou and Wu in [Hou T.Y., Wu X.-H., A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comput. Phys., 1997, 134(1), 169–189] to the PDE system of linear elasticity. The application, motivated by the multiscale analysis of highly heterogeneous composite materials, is twofold. Resolving the heterogeneities on the finest scale, we utilize the linear MsFEM basis for the...

On discontinuous Galerkin method and semiregular family of triangulations

Aleš Prachař (2006)

Applications of Mathematics

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Discretization of second order elliptic partial differential equations by discontinuous Galerkin method often results in numerical schemes with penalties. In this paper we analyze these penalized schemes in the context of quite general triangular meshes satisfying only a semiregularity assumption. A new (modified) penalty term is presented and theoretical properties are proven together with illustrative numerical results.