Abstract
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.
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Communicated by: Zhongying Chen.
Dedicated to Prof. Wolfgang L. Wendland in occasion of his 75th birthday.
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Baroli, D., Quarteroni, A. & Ruiz-Baier, R. Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity. Adv Comput Math 39, 425–443 (2013). https://doi.org/10.1007/s10444-012-9286-8
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DOI: https://doi.org/10.1007/s10444-012-9286-8
Keywords
- Nonlinear elasticity
- Discontinuous Galerkin formulation
- Incompressible material
- Edge-based stabilization