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Mathematical analysis of a penalisation strategy for incompressible elastodynamics
Asymptotic Analysis ( IF 1.4 ) Pub Date : 2020-05-18 , DOI: 10.3233/asy-201617
F. Caforio 1, 2 , S. Imperiale 1, 2
Affiliation  

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.

中文翻译:

不可压缩弹性动力学惩罚策略的数学分析

这项工作解决了数学分析 - 通过渐近分析 - 作者最近开发的准不可压缩介质中弹性波传播问题的完全离散化的惩罚策略。当惩罚参数趋于无穷大时,我们对惩罚问题的连续版本的解向其形式极限提供了收敛分析。此外,作为基本的中间步骤,我们提供了当不可压缩参数趋于无穷大时,准不可压缩问题的解向纯不可压缩问题的解的收敛性的渐近分析。最后,我们进一步详细说明了保证上述收敛成立所需的规律性假设。
更新日期:2020-05-18
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