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

Leugering G, Friederich J, Steinmann P (2012)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2012

Journal

GAMM-Mitteilungen Wiley-VCH Verlag

Book Volume: 35

Pages Range: 175-190

Journal Issue: 2

DOI: 10.1002/gamm.201210012

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. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA.

Authors with CRIS profile

Günter Leugering Lehrstuhl für Angewandte Mathematik Jan Friederich Lehrstuhl für Technische Mechanik Paul Steinmann Lehrstuhl für Technische Mechanik

How to cite

APA:

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

MLA:

Leugering, Günter, Jan Friederich, and Paul Steinmann. "Adaptive refinement based on asymptotic expansions of finite element solutions for node insertion in 1d." GAMM-Mitteilungen 35.2 (2012): 175-190.

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