Lecture SS 21 Advanced Topics in Numerical Analysis
The lecture course will investigate homogenization methods for the solution of partial differential equations with rapidly oscillating coefficients. The goal of these methods is to avoid the spatial resolution of all details at the finest scale. To this end the effective material behaviour is evaluated on macroscopic quadrature nodes prior to the actual finite element computations. These effective properties are then used in finite element computations on the macroscale. The lecture course will derive these methods and study a priori and a posteriori error estimate. Furthermore, reduced basis methods will be presented and analysed.
For participants interested in the numerical implementation of these methods there will be an accompanying practical lab.