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Numerical solution of the stationary diffusion equation by means of homogenization

 
: Kabel, Matthias; Struckmeier, Jens

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Fulltext (PDF; )

Hamburg: Universität Hamburg, 2007, 33 pp.
Hamburger Beiträge zur angewandten Mathematik, 2007, 20
English
Report, Electronic Publication
Fraunhofer ITWM ()

Abstract
For elliptic partial differential equations with periodically oscillating coefficients quadratic L2-convergence of a corrected asymptotic expansion, which is motivated by the theory of homogenization, is proven in the one-dimensional case.
In the two-dimensional case the rate of convergence and its dependency on the symmetry of the diffusion coefficient is numerically analysed. The correction of the asymptotic expansion on a locally refined grid is then embedded inside a two-grid method and numerically compared with a classical PCG-method.

: http://publica.fraunhofer.de/documents/N-473356.html