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Author: Reichelt, Sina × Subject: error estimates ×

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Now showing 1 - 3 of 3
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    Error estimates for elliptic equations with not exactly periodic coefficients
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Reichelt, Sina
    This note is devoted to the derivation of quantitative estimates for linear elliptic equations with coefficients that are not exactly ε-periodic and the ellipticity constant may degenerate for vanishing ε. Here ε>0 denotes the ratio between the microscopic and the macroscopic length scale. It is shown that for degenerating and non-degenerating coefficients the error between the original solution and the effective solution is of order √ε. Therefore suitable test functions are constructed via the periodic unfolding method and a gradient folding operator making only minimal additional assumptions on the given data and the effective solution with respect to the macroscopic scale.
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    Corrector estimates for a class of imperfect transmission problems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Reichelt, Sina
    Based on previous homogenization results for imperfect transmission problems in two-component domains with periodic microstructure, we derive quantitative estimates for the difference between the microscopic and macroscopic solution. This difference is of order , where > 0 describes the periodicity of the microstructure and 2 (0; 1/2 ] depends on the transmission condition at the interface between the two components. The corrector estimates are proved without assuming additional regularity for the local correctors using the periodic unfolding method.
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    Error estimates for nonlinear reaction-diffusion systems involving different diffusion length scales
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Reichelt, Sina
    We derive quantitative error estimates for coupled reaction-diffusion systems, whose coefficient functions are quasi-periodically oscillating modeling microstructure of the underlying macroscopic domain. The coupling arises via nonlinear reaction terms, and we allow for different diffusion length scales, i.e. whereas some species have characteristic diffusion length of order 1, other species may diffuse much slower, namely, with order of the characteristic microstructure-length scale. We consider an effective system, which is rigorously obtained via two-scale convergence, and we prove that the error of its solution to the original solution is of order 1/2.