THE PARTIAL HOMOGENIZATION: CONTINUOUS AND SEMI-DISCRETIZED VERSIONS
Grigory P. Panasenko · Mathematical Models and Methods in Applied Sciences · 2007
The partial homogenization is a new method for the treatment of the boundary layers in the homogenization theory. It keeps the initial formulation near the boundary, passes to the high order homogenization at some distance from the boundary and prescribes the asymptotically precise junction conditions between the homogenized and the heterogeneous models at the interface. This method is related to the method of asymptotic partial domain decomposition MAPDD (see G. Panasenko, Method of asymptotic partial decomposition of domain, Math. Mod. Meth. Appl. Sci.8 (1998) 139–156). The partial homogenization (as well as the MAPDD) can be interpreted as a multi-scale model coupling the homogenized (macroscopic) description in the internal main part of the domain and the microscopic zoom in the domain of the location of the boundary layers. The semi-discretized partial homogenization uses some high order finite element projection in the homogenized subdomain.