On a variant of random homogenization theory: convergence of the residual process and approximation of the homogenized coefficients (Q2877381)
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scientific article; zbMATH DE number 6333649
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a variant of random homogenization theory: convergence of the residual process and approximation of the homogenized coefficients |
scientific article; zbMATH DE number 6333649 |
Statements
On a variant of random homogenization theory: convergence of the residual process and approximation of the homogenized coefficients (English)
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22 August 2014
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stochastic homogenization
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random stationary diffeomorphisms
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central limit theorem
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approximation of homogenized coefficients
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0.9065334
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0.8915056
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0.88316435
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0.8818621
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0.88176954
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0.88122046
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0.88006675
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The authors study a linear second-order elliptic equation in divergence form driven by an oscillatory stochastic matrix \(A\). Assuming that \(A\) is the composition of a periodic matrix and of a stochastic diffeomorphism, they apply homogenization theory and calculate the homogenized matrix by solving the corrector problem on the entire space. The main result of the paper is the proof for an explicit rate of convergence towards zero of the residual process, which is the difference between the solution to the oscillatory problem and the solution to the homogenized problem.
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