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