WIAS Preprint No. 2260, (2016)

Error estimates for elliptic equations with not exactly periodic coefficients



Authors

  • Reichelt, Sina

2010 Mathematics Subject Classification

  • 35B10 35B27 35B40 35D30 35J70

Keywords

  • homogenization, error estimates, periodic unfolding, gradient folding operator

Abstract

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.

Appeared in

  • Adv. Math. Sci. Appl., 25 (2016), pp. 117--131.

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