<div class="csl-bib-body">
<div class="csl-entry">Geiersbach, C., Heitzinger, C., & Tulzer, G. (2016). Optimal Approximation of the First-Order Corrector in Multiscale Stochastic Elliptic PDE. <i>SIAM/ASA Journal on Uncertainty Quantification</i>, <i>4</i>(1), 1246–1262. https://doi.org/10.1137/16M106011X</div>
</div>
-
dc.identifier.issn
2166-2525
-
dc.identifier.uri
http://hdl.handle.net/20.500.12708/148100
-
dc.description.abstract
This work addresses the development of an optimal computational scheme for the approximation of the first-order corrector arising in the stochastic homogenization of linear elliptic PDEs in diver- gence form. Equations of this type describe, for example, diffusion phenomena in materials with a heterogeneous microstructure, but require enormous computational efforts in order to obtain reliable results. We derive an optimization problem for the needed computational work with a given error tolerance, then extract the governing parameters from numerical experiments, and finally solve the obtained optimization problem. The numerical approach investigated here is a stochastic sampling scheme for the probability space connected with a finite-element method for the discretization of the physical space.
en
dc.description.sponsorship
FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
-
dc.language.iso
en
-
dc.publisher
SIAM PUBLICATIONS
-
dc.relation.ispartof
SIAM/ASA Journal on Uncertainty Quantification
-
dc.subject
Multiscale problems
en
dc.subject
Numerical stochastic homogenization
en
dc.subject
Optimization
en
dc.subject
Stochastic elliptic PDE
en
dc.title
Optimal Approximation of the First-Order Corrector in Multiscale Stochastic Elliptic PDE