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Diamond elements: a finite element/discrete-mechanics approximation scheme with guaranteed optimal convergence in incompressible elasticity

Hauret, P. and Kuhl, E. and Ortiz, M. (2007) Diamond elements: a finite element/discrete-mechanics approximation scheme with guaranteed optimal convergence in incompressible elasticity. International Journal for Numerical Methods in Engineering, 72 (3). pp. 253-294. ISSN 0029-5981. http://resolver.caltech.edu/CaltechAUTHORS:20171121-135247808

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Abstract

We present a finite element discretization scheme for the compressible and incompressible elasticity problems that possess the following properties: (i) the discretization scheme is defined on a triangulation of the domain; (ii) the discretization scheme is defined—and is identical—in all spatial dimensions; (iii) the displacement field converges optimally with mesh refinement; and (iv) the inf–sup condition is automatically satisfied. The discretization scheme is motivated both by considerations of topology and analysis, and it consists of the combination of a certain mesh pattern and a choice of interpolation that guarantees optimal convergence of displacements and pressures. Rigorous proofs of the satisfaction of the inf–sup condition are presented for the problem of linearized incompressible elasticity. We additionally show that the discretization schemes can be given a compelling interpretation in terms of discrete differential operators. In particular, we develop a discrete analogue of the classical tensor differential complex in terms of which the discrete and continuous boundary-value problems are formally identical. We also present numerical tests that demonstrate the dimension-independent scope of the scheme and its good performance in problems of finite elasticity.


Item Type:Article
Related URLs:
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https://dx.doi.org/10.1002/nme.1992DOIArticle
http://onlinelibrary.wiley.com/doi/10.1002/nme.1992/fullPublisherArticle
Additional Information:© 2007 John Wiley & Sons. Received 15 February 2006; Revised 11 August 2006; Accepted 23 October 2006. We gratefully acknowledge the support of the Department of Energy through Caltech’s ASCI/ASAPCenter for Simulating the Dynamic Response of Materials.
Group:GALCIT
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Funding AgencyGrant Number
Department of Energy (DOE)UNSPECIFIED
Subject Keywords:incompressible elasticity; inf–sup condition; macroelements; discrete mechanics
Record Number:CaltechAUTHORS:20171121-135247808
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20171121-135247808
Official Citation:Hauret, P., Kuhl, E. and Ortiz, M. (2007), Diamond elements: a finite element/discrete-mechanics approximation scheme with guaranteed optimal convergence in incompressible elasticity. Int. J. Numer. Meth. Engng., 72: 253–294. doi:10.1002/nme.1992
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83402
Collection:CaltechAUTHORS
Deposited By: Lydia Suarez
Deposited On:22 Nov 2017 19:15
Last Modified:22 Nov 2017 19:15

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