TY - GEN A1 - Eigel, Martin A1 - Peterseim, Daniel T1 - A Network FEM for composite materials with a posterior error control N2 - A novel Finite Element Method (FEM) for the computational simulation in particle reinforced composite materials with many inclusions is presented. It is based on an adapted mesh which consists of triangles and parametric quadrilaterals in 2D. The number of elements and, hence, the number of degrees of freedom are proportional to the number of inclusions. The error of the method is independent of the distance of the neighboring inclusions. While being related to network methods, the approach can tackle more general settings. We present an efficient residual a posteriori error estimator which enables to compute reliable upper and lower error bounds. Several numerical examples illustrate the performance of the method and the error estimator. Moreover, it is demonstrated that the assumption of a lattice structure of inclusions can easily lead to incorrect predictions about material properties. KW - A posteriori, error analysis, finite element method, composite material, multiscale, high contrast, generalized Delaunay, network Y1 - 2012 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1172 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-11721 ER -