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Published in:
Implicit Boundary and Adaptive Anisotropic Meshing Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Anisotropic, Adaptive Finite Elements for a Thin 3D Plate

Authors : Marco Picasso, Adrien Loseille

Published in: New Challenges in Grid Generation and Adaptivity for Scientific Computing

Publisher: Springer International Publishing

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Abstract

An adaptive, anisotropic finite element algorithm is proposed to solve the 3D linear elasticity equations in a thin 3D plate. Numerical experiments show that adaptive computations can be performed in thin 3D domains having geometrical aspect ratio 1:1000.

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previous chapter On the Generation of Curvilinear Meshes Through Subdivision of Isoparametric Elements
next chapter Anisotropic Mesh and Time Step Adaptivity for Solute Transport Modeling in Porous Media
Literature
1.
Cao, W.: Superconvergence analysis of the linear finite element method and a gradient recovery postprocessing on anisotropic meshes. Math. Comp. 84(291), 89–117 (2015)CrossRefMATHMathSciNet
2.
3.
4.
Frey, P., George, P.L.: Mesh generation. Application to finite elements, 2nd edn. ISTE Ltd and John Wiley & Sons, New York (2008)
5.
Hachem, E., Kloczko, T., Digonnet, H., Coupez, T.: Stabilized finite element solution to handle complex heat and fluid flows in industrial furnaces using the immersed volume method. Int. J. Numer. Methods Fluids 68(1), 99–121 (2012)CrossRefMATHMathSciNet
6.
Hassan, W.: Algorithmes d’adaptation de maillages anisotropes et application l’aérodynamique. Ph.D. thesis, EPFL, 1015 Lausanne, Switzerland (2012). Nb. 5304
7.
8.
Kunert, G.: A posteriori \(L_{2}\) error estimation on anisotropic tetrahedral finite element meshes. IMA J. Numer. Anal. 21(2), 503–523 (2001)CrossRefMATHMathSciNet
9.
Loseille, A.: Adaptation de maillage anisotrope 3D multi-échelles et ciblée à une fonctionnelle pour la mécanique des fluides. Ph.D. thesis, University Paris VI (2008)
10.
Loseille, A., Alauzet, F.: Continuous mesh framework part i: Well-posed continuous interpolation error. SIAM J. Numer. Anal. 49(1), 38–60 (2011)CrossRefMATHMathSciNet
11.
Loseille, A., Dervieux, A., Alauzet, F.: Fully anisotropic goal-oriented mesh adaptation for 3D steady Euler equations. J. Comput. Phys. 229(8), 2866–2897 (2010)CrossRefMATHMathSciNet
12.
Loseille, A., Löhner, R.: Adaptive anisotropic simulations in aerodynamics. AIAA-10-0169 (2010)
13.
Loseille, A., Löhner, R.: Anisotropic mesh generation for high-fidelity simulations in cfd. INRIA Preprint (2014)
14.
Picasso, M.: An anisotropic error indicator based on Zienkiewicz-Zhu error estimator: application to elliptic and parabolic problems. SIAM J. Sci. Comp. 24, 1328–1355 (2003)CrossRefMATHMathSciNet
15.
Picasso, M.: Adaptive finite elements with large aspect ratio based on an anisotropic error estimator involving first order derivatives. Comput. Methods Appl. Mech. Eng. 196(1-3), 14–23 (2006)CrossRefMATHMathSciNet
16.
Piggott, M.D., Farrell, P.E., Wilson, C.R., Gorman, G.J., Pain, C.C.: Anisotropic mesh adaptivity for multi-scale ocean modelling. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 367(1907), 4591–4611 (2009)CrossRefMATHMathSciNet
Metadata
Title
Anisotropic, Adaptive Finite Elements for a Thin 3D Plate
Authors
Marco Picasso
Adrien Loseille
Copyright Year
2015
Book
New Challenges in Grid Generation and Adaptivity for Scientific Computing

Print ISBN: 978-3-319-06052-1

Electronic ISBN: 978-3-319-06053-8

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-06053-8_11

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