A Network FEM for composite materials with a posterior error control

Please always quote using this URN:urn:nbn:de:0296-matheon-11721
  • 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.

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Metadaten
Author:Martin Eigel, Daniel Peterseim
URN:urn:nbn:de:0296-matheon-11721
Referee:Ralf Kornhuber
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/09/28
Release Date:2012/09/28
Tag:A posteriori, error analysis, finite element method, composite material, multiscale, high contrast, generalized Delaunay, network
Institute:Humboldt-Universität zu Berlin
Zuse Institute Berlin (ZIB)
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N15 Error bounds
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Qxx Homogenization, determination of effective properties / 74Q20 Bounds on effective properties
Preprint Number:985
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