In this work, the multiscale problem of modeling fluctuations in boundary layers in stochastic elliptic partial differential equations is solved by homogenization. A homogenized equation for the covariance of the solution of stochastic elliptic PDEs is derived. In addition to the homogenized equation, a rate for the covariance and variance as the cell size tends to zero is given. For the homogenized problem, an existence and uniqueness result and further properties are shown. The multiscale problem stems from the modeling of the electrostatics in nanoscale field-effect sensors, where the fluctuations arise from random charge concentrations in the cells of a boundary layer. Finally, numerical results and a numerical verification are presented. © 2014 International Press.
Bibliographical noteKAUST Repository Item: Exported on 2021-09-21
Acknowledged KAUST grant number(s): KUK-I1007-43
Acknowledgements: This work was supported by the FWF (Austrian Science Fund) project No. P20871-N13 and by the WWTF (Viennese Science and Technology Fund) project No. MA09-028. This publication is based on work supported by Award No. KUK-I1007-43, funded by the King Abdullah University of Science and Technology (KAUST). This work was supported by the NSF under grants DMS-0604986 and DMS-0757309.
ASJC Scopus subject areas
- Applied Mathematics