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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