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Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity

Baroli, Davide ; Quarteroni, Alfio ; Ruiz-Baier, Ricardo

In: Advances in Computational Mathematics, 2013, vol. 39, no. 2, p. 425-443

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    Title
    • Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity
    Author
    • Baroli, Davide. Dipartimento di Fisica e Matematica, Università degli studi dell'Insubria, Via Valleggio 11, 22100, Como, Italy
    • Quarteroni, Alfio. CMCS-MATHICSE-SB, Ecole Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland
    • Ruiz-Baier, Ricardo. CMCS-MATHICSE-SB, Ecole Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Advances in Computational Mathematics, 2013, vol. 39, no. 2, p. 425-443. Springer US; http://www.springer-ny.com
    Other Version
    OAI-PMH Identifier
    • oai:doc.rero.ch:312548
    Summary
    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