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Numerical solution of the stationary diffusion equation by means of homogenization

: Kabel, Matthias; Struckmeier, Jens

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

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.