Composite finite elements for problems containing small geometric details

In this paper, we will present efficient strategies how composite finite elements can be realized for the discretization of PDEs on domains containing small geometric details. In contrast to standard finite elements, the minimal dimension of this new class of finite element spaces is completely independent of the number of geometric details of the physical domains. Hence, it allows coarse level discretization of PDEs which can be used, e.g., preferably for multi-grid methods and homogenization of PDEs in non-periodic situations.