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Convergent numerical schemes for the compressible hyperelastic rod wave equation

Cohen, David ; Raynaud, Xavier

In: Numerische Mathematik, 2012, vol. 122, no. 1, p. 1-59

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    Titre
    • Convergent numerical schemes for the compressible hyperelastic rod wave equation
    Auteur
    • Cohen, David. Mathematisches Institut, Universität Basel, 4051, Basel, Switzerland
    • Raynaud, Xavier. Center of Mathematics for Applications, University of Oslo, 0316, Oslo, Norway
    Type de document
    • Postprint
    Classification
    • Informatique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:321825
    Summary
    We propose a fully discretised numerical scheme for the hyperelastic rod wave equation on the line. The convergence of the method is established. Moreover, the scheme can handle the blow-up of the derivative which naturally occurs for this equation. By using a time splitting integrator which preserves the invariants of the problem, we can also show that the scheme preserves the positivity of the energy density