The Convergence Rate of Iterative Procedures for Elliptic Problems in Heterogeneous Media

Alexandre Sant Francisco; Helio Pedro Amaral Souto; Thiago Jordem Pereira

doi:10.4028/www.scientific.net/DDF.353.298

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The Convergence Rate of Iterative Procedures for Elliptic Problems in Heterogeneous Media

Abstract:

We investigate the convergence rate of two iterative procedures that approximate the solutionof fluid flow problems in heterogeneous porous media. Porous media flows at large scales arecomplex problems, which require fine grid solutions to provide accurate results. Pressures and velocitiesassociated to these problems are governed by second order elliptic equations. We discretizesuch equations by a mixed and hybrid finite element method, combined with domain-decompositioniterative procedures. In order to minimize the computational effort involved in the numerical approximation,we have presented an iterative procedure to accelerate the convergence rate in the approximation.In this paper, we perform numerical experiments to compare iterative procedures in order tocheck which one provides the best convergence rate. We believe that steady-state diffusion problemscan be solved efficient and accurately by the most robust procedure.

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Periodical:

Defect and Diffusion Forum (Volume 353)

Pages:

298-305

DOI:

https://doi.org/10.4028/www.scientific.net/DDF.353.298

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Online since:

May 2014

Authors:

Alexandre Sant Francisco, Helio Pedro Amaral Souto, Thiago Jordem Pereira

Keywords:

Domain Decomposition, Elliptic Equations, Porous Media

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