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3D composite finite elements for elliptic boundary value problems with discontinuous coefficients


Preusser, T; Rumpf, M; Sauter, S; Schwen, L O (2011). 3D composite finite elements for elliptic boundary value problems with discontinuous coefficients. SIAM Journal on Scientific Computing (SISC), 33(5):2115-2143.

Abstract

For scalar and vector-valued elliptic boundary value problems with discontinuous
coefficients across geometrically complicated interfaces, a composite finite element approach is developed.
Composite basis functions are constructed, mimicing the expected jump condition for the
solution at the interface in an approximate sense. The construction is based on a suitable local
interpolation on the space of admissible functions. We study the order of approximation and the
convergence properties of the method numerically. As applications, heat diffusion in an aluminium
foam matrix filled with polymer and linear elasticity of micro-structured materials, in particular
specimens of trabecular bone, are investigated. Furthermore, a numerical homogenization approach
is developed for periodic structures and real material specimens which are not strictly periodic but
are considered as statistical prototypes. Thereby, effective macroscopic material properties can be
computed.

Abstract

For scalar and vector-valued elliptic boundary value problems with discontinuous
coefficients across geometrically complicated interfaces, a composite finite element approach is developed.
Composite basis functions are constructed, mimicing the expected jump condition for the
solution at the interface in an approximate sense. The construction is based on a suitable local
interpolation on the space of admissible functions. We study the order of approximation and the
convergence properties of the method numerically. As applications, heat diffusion in an aluminium
foam matrix filled with polymer and linear elasticity of micro-structured materials, in particular
specimens of trabecular bone, are investigated. Furthermore, a numerical homogenization approach
is developed for periodic structures and real material specimens which are not strictly periodic but
are considered as statistical prototypes. Thereby, effective macroscopic material properties can be
computed.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2011
Deposited On:21 Sep 2011 09:17
Last Modified:17 Feb 2018 13:39
Publisher:Society for Industrial and Applied Mathematics (SIAM)
ISSN:1064-8275
Additional Information:Copyright © 2011, Society for Industrial and Applied Mathematics
OA Status:Green
Publisher DOI:https://doi.org/10.1137/100791750
Official URL:http://epubs.siam.org/sisc/

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