Composite finite elements for the approximation of PDEs on domains with complicated micro-structures
The implementation of multigrid methods requires the use of hierarchical grids, from coarse to fine grids. Thus, these multigrid methods are well adapted to problems involving regular domains. In the case of domains with micro-structures, the basic multigrid method is no longer applicable since coarse meshes cannot take into account such micro-structures. The object of this paper is to introduce and to analyse mathematically finite element tools useful to extend such multigrid methods to partial differential equations (PDEs) formulated on domains with complicated micro-structures. A second forthcoming paper will present the effective implementation of such extensions.
scientific article; zbMATH DE number 1027744