Quantitative Homogenization and Averaging

• Applicant: Professor Dr. Bernold Fiedler
• Subject Area: Mathematics
• Term: from 2000 to 2009
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5276083

Analysis of partial differential equations with rapidly oscillating coefficients in time and/or space aims at eliminating these dependencies by averaging or homogenization techniques. For systems of parabolic and elliptic type we aim at a quantitative comparison with the averaged or homogenized equations. Periodic and quasiperiodic inhomogenities with Diophantine frequencies will be considered.With a single spatial homogenization step, we expect errors of fractional order eg for oscillation scale e and suitable g smaller than 1. With sufficiently many time averaging steps we expect errors of exponential order exp(-c/eb), for some b larger than 0.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1095: Analysis, Modeling and Simulation of Multiscale Problems