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Pré-Publication, Document De Travail Année : 2019

A stiffly stable semi-discrete scheme for the characteristic linear hyperbolic relaxation with boundary

Résumé

We study the stability of the semi-discrete central scheme for the linear damped wave equation with boundary. We exhibit a sufficient condition on the boundary to guarantee the uniform stability of the initial boundary value problem for relaxation system independent of stiffness of the source term and of the space step. The boundary is approximated using a summation-by-parts method and the stiff stability is proved by energy estimates and Laplace transform. We also investigate if the condition is also necessary, following the continuous case studied by Xin and Xu (2000).
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Dates et versions

hal-02136776 , version 1 (22-05-2019)
hal-02136776 , version 2 (20-02-2020)

Identifiants

  • HAL Id : hal-02136776 , version 1

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Benjamin Boutin, Thi Hoai Thuong Nguyen, Nicolas Seguin. A stiffly stable semi-discrete scheme for the characteristic linear hyperbolic relaxation with boundary. 2019. ⟨hal-02136776v1⟩
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