A two-dimensional flea on the elephant phenomenon and its numerical visualization
Bianchini R, Gosse L, Zuazua E (2019)
Publication Type: Journal article
Publication year: 2019
Journal
Book Volume: 17
Pages Range: 137-166
Journal Issue: 1
DOI: 10.1137/18M1179985
Abstract
Localization phenomena (sometimes called flea on the elephant) for the operator Lvarepsilon = varepsilon 2Δ u + p(x)u, p(x) being an asymmetric double well potential, are studied both analytically and numerically, mostly in two space dimensions within a perturbative framework. Starting from a classical harmonic potential, the effects of various perturbations are retrieved, especially in the case of two asymmetric potential wells. These findings are illustrated numerically by means of an original algorithm, which relies on a discrete approximation of the Steklov-Poincaré operator for Lvarepsilon, and for which error estimates are established. Such a two-dimensional discretization produces less mesh imprinting than more standard finite differences and correctly captures sharp layers.
Authors with CRIS profile
Involved external institutions
École normale supérieure de Lyon (ENS)
France (FR)
Institute for Applied Mathematics Mauro Picone / Istituto per le Applicazioni del Calcolo Mauro Picone
Italy (IT)
University of Deusto / Universidad de Deusto
Spain (ES)
France (FR)
Institute for Applied Mathematics Mauro Picone / Istituto per le Applicazioni del Calcolo Mauro Picone
Italy (IT)
University of Deusto / Universidad de Deusto
Spain (ES)
How to cite
APA:
Bianchini, R., Gosse, L., & Zuazua, E. (2019). A two-dimensional flea on the elephant phenomenon and its numerical visualization. Multiscale Modeling & Simulation, 17(1), 137-166. https://dx.doi.org/10.1137/18M1179985
MLA:
Bianchini, Roberta, Laurent Gosse, and Enrique Zuazua. "A two-dimensional flea on the elephant phenomenon and its numerical visualization." Multiscale Modeling & Simulation 17.1 (2019): 137-166.
BibTeX: Download