Adaptive refinement based on asymptotic expansions of finite element solutions for node insertion in 1d

Friedrich, J., Leugering, G. and Steinmann, P. (2012) Adaptive refinement based on asymptotic expansions of finite element solutions for node insertion in 1d. GAMM Mitteilungen, 35(2), pp. 175-190. (doi: 10.1002/gamm.201210012)

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Abstract

We consider refinement of finite element discretizations by splitting nodes along edges. For this process, we derive asymptotic expansions of Galerkin solutions of linear second-order elliptic equations. Thereby, we calculate a topological derivative w.r.t. node insertion for functionals such as the total potential energy, minimization of which decreases the approximation error in the energy norm. Hence, these sensitivities can be used to define indicators for local h-refinement. Our results suggest that this procedure leads to an efficient adaptive refinement method. This presentation is concerned with a model problem in 1d. The extension of this concept to higher dimensions will be the subject of forthcoming publications.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Steinmann, Professor Paul
Authors: Friedrich, J., Leugering, G., and Steinmann, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:GAMM Mitteilungen
Publisher:Wiley
ISSN:0936-7195
ISSN (Online):1522-2608

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