Mathematical analysis of a penalization strategy for incompressible elastodynamics

Abstract : This work addresses the mathematical analysis - by means of asymptotic analysis - of a penalisation strategy for the full discretisation of elastic wave propagation problems in quasi-incompressible media that has been recently developed by the authors. We provide a convergence analysis of the solution of the continuous version of the penalised problem towards its formal limit when the penalisation parameter tends to infinity. Moreover, as a fundamental intermediate step we provide an asymptotic analysis of the convergence of solutions of quasi-incompressible problems towards solutions of purely incompressible problems when the incompressibility parameter tends to infinity. Finally, we further detail the regularity assumptions required to guarantee that the mentioned convergence holds.
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https://hal.inria.fr/hal-02389286
Contributor : Sébastien Imperiale <>
Submitted on : Monday, December 2, 2019 - 2:29:14 PM
Last modification on : Wednesday, December 4, 2019 - 1:20:57 AM

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  • HAL Id : hal-02389286, version 1

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F Caforio, Sébastien Imperiale. Mathematical analysis of a penalization strategy for incompressible elastodynamics. 2019. ⟨hal-02389286⟩

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