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End date: 2019 × Start date: 2011 × DDC: 510 × Subject: error estimates × Subject: periodic unfolding ×

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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.