Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity

In this paper we present a discontinuous Galerkin method applied to incompressible nonlinear elastostatics in a total Lagrangian deformation-pressure formulation, for which a suitable interior penalty stabilization is applied. We prove that the proposed discrete formulation for the linearized problem is well-posed, asymptotically consistent and that it converges to the corresponding weak solution. The derived convergence rates are optimal and further confirmed by a set of numerical examples in two and three spatial dimensions.


Published in:
Advances in Computational Mathematics, 39, 425-443
Year:
2013
Publisher:
New York, Springer Verlag
ISSN:
1019-7168
Keywords:
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 Record created 2012-02-10, last modified 2018-03-17

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