The Mathematical Institute, University of Oxford, Eprints Archive

Error estimation and adaptivity for incompressible, non–linear (hyper–)elasticity

Whiteley, J. P. and Tavener, S. J. (2012) Error estimation and adaptivity for incompressible, non–linear (hyper–)elasticity. Computer Methods in Applied Mechanics and Engineering . (Submitted)



A Galerkin finite element method is developed for non–linear, incompressible (hyper) elasticity, and a posteriori error estimates are derived for both linear functionals of the solution and linear functionals of the stress on a boundary where Dirichlet boundary conditions are applied. A second, higher order method for calculating a linear functional of the stress on a Dirichlet boundary is also presented together with an a posteriori error estimator for this approach. An implementation for a 2D model problem with known solution demonstrates the accuracy of the error estimators. Finally the a posteriori error estimate is shown to provide a basis for effective mesh adaptivity.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1594
Deposited By: Peter Hudston
Deposited On:01 Sep 2012 07:40
Last Modified:29 May 2015 19:17

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