Session B6 - Multiresolution and Adaptivity in Numerical PDEs
July 13, 18:00 ~ 18:25 - Room T1
Computation of local and quasi-local effective diffusion tensors in elliptic homogenization
University of Bonn, Germany - email@example.com
The talk discusses a re-interpretation of existing multiscale methods by means of a discrete integral operator acting on standard finite element spaces. The exponential decay of the involved integral kernel motivates the use of a diagonal approximation and, hence, a localized piecewise constant effective coefficient. This local model turns out to be appropriate when the localized coefficient satisfies a certain homogenization criterion, which can be verified a posteriori. An a priori error analysis of the local model is presented and illustrated in numerical experiments.
Reference: D. Gallistl and D. Peterseim: Computation of local and quasi-local effective diffusion tensors in elliptic homogenization. ArXiv e-print 1608.02092, 2016.
Joint work with Dietmar Gallistl (Karlsruhe Institute of Technology, Germany).