An adaptive finite element method based on sensitivities for node insertion

Friederich J, Leugering G, Steinmann P (2012)


Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2012

Journal

Publisher: Wiley - V C H Verlag GmbbH & Co.

Book Volume: 35

Pages Range: 175-190

Journal Issue: 2

URI: http://onlinelibrary.wiley.com/doi/10.1002/gamm.201210012/full

DOI: 10.1002/gamm.201210012

Open Access Link: http://onlinelibrary.wiley.com/doi/10.1002/gamm.201210012/epdf

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 approxi-
mation 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 re-
finement 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.

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How to cite

APA:

Friederich, J., Leugering, G., & Steinmann, P. (2012). An adaptive finite element method based on sensitivities for node insertion. GAMM-Mitteilungen, 35(2), 175-190. https://doi.org/10.1002/gamm.201210012

MLA:

Friederich, Jan, Günter Leugering, and Paul Steinmann. "An adaptive finite element method based on sensitivities for node insertion." GAMM-Mitteilungen 35.2 (2012): 175-190.

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