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IMA Journal of Numerical Analysis Advance Access originally published online on May 9, 2008
IMA Journal of Numerical Analysis 2009 29(2):404-420; doi:10.1093/imanum/drn013
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Inf–sup stable finite-element pairs based on dual meshes and bases for nearly incompressible elasticity

Bishnu P. Lamichhane{dagger}

Department of Engineering and Applied Science, University of Aston, Aston Triangle, Birmingham B4 7ET, UK

{dagger} Email: blamichha{at}yahoo.com

Received on 30 April 2007. Revised on 10 December 2007.


  Abstract

We consider finite-element methods based on simplices to solve the problem of nearly incompressible elasticity. Two different approaches based, respectively, on dual meshes and dual bases are presented, where in both approaches pressure is discontinuous and can be statically condensed out from the system. These novel approaches lead to displacement-based low-order finite-element methods for nearly incompressible elasticity based on rigorous mathematical framework. Numerical results are provided to demonstrate the efficiency of the approach.

Key Words: mixed finite elements; nodal average pressure; nearly incompressible elasticity; dual bases; dual meshes


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