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IMA Journal of Numerical Analysis Advance Access published online on March 13, 2009
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drn069
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Discretization error and modelling error in the context of the rapid inflation of hyperelastic membranes

S. Shaw{dagger}, M. K. Warby and J. R. Whiteman

Brunel Institute of Computational Mathematics and Mathematical Sciences, Brunel University, Uxbridge UB8 3PH, UK

{dagger} Corresponding author. Email: simon.shaw{at}brunel.ac.uk

Received on 12 June 2008. Revised on 30 September 2008.


  Abstract

The computational modelling of the rapid large inflation of hyperelastic circular sheets modelled as axisymmetric membranes is treated, with the aim of estimating engineering quantities of interest and their errors. Fine (involving inertia terms) and coarse (quasi-static) models of the inflation are considered and, using goal-oriented techniques, both modelling and discretization errors are estimated. Numerical results involving only discretization errors for the quasi-static problem and both modelling and discretization errors for the dynamic problem are presented.

Key Words: finite-element method; finite deformation; a posteriori modelling error estimates; a posteriori discretization error estimates

This paper is dedicated to A. R. Mitchell, colleague, mentor and friend over many years


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