Boundary Layer Estimates in Stochastic Homogenization
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915901686677504 |
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| author | Bella, Peter Fischer, Julian Josien, Marc Raithel, Claudia |
| author_facet | Bella, Peter Fischer, Julian Josien, Marc Raithel, Claudia |
| contents | We prove quantitative decay estimates for the boundary layer corrector in stochastic homogenization in the case of a half-space boundary. Our estimates are of optimal order and show that the gradient of the boundary layer corrector features nearly fluctuation-order decay; its expected value decays even one order faster. As a corollary, we deduce estimates on the accuracy of the representative volume element (RVE) method for the computation of effective coefficients: in $d\geq 3$ dimensions our understanding of the decay of boundary layers enables us to justify an improved formula for the RVE method, based on a combination of oversampling with the Hill-Mandel condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12911 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary Layer Estimates in Stochastic Homogenization Bella, Peter Fischer, Julian Josien, Marc Raithel, Claudia Analysis of PDEs 35J25, 60K37, 60H25 We prove quantitative decay estimates for the boundary layer corrector in stochastic homogenization in the case of a half-space boundary. Our estimates are of optimal order and show that the gradient of the boundary layer corrector features nearly fluctuation-order decay; its expected value decays even one order faster. As a corollary, we deduce estimates on the accuracy of the representative volume element (RVE) method for the computation of effective coefficients: in $d\geq 3$ dimensions our understanding of the decay of boundary layers enables us to justify an improved formula for the RVE method, based on a combination of oversampling with the Hill-Mandel condition. |
| title | Boundary Layer Estimates in Stochastic Homogenization |
| topic | Analysis of PDEs 35J25, 60K37, 60H25 |
| url | https://arxiv.org/abs/2403.12911 |