Spectral element schemes for the Korteweg-de Vries and Saint-Venant equations

Résumé : Hyperbolic systems and dispersive equations remain challenging for finite element methods (FEMs). On the basis of an arbitrarily high order FEM, namely the spectral element method (SEM), we address : -The Korteweg-de Vries equation, to explain how high order derivative terms can be efficiently handled with a C0-continuous Galerkin approximation. The conservation of the invariants is also focused on, especially by using in time embedded implicit-explicit Runge Kutta schemes. -The 2D shallow water equations, to show how a stabilized SEM can solve problems involving shocks. We especially focus on flows involving dry-wet transitions and propose to this end an efficient variant of the entropy viscosity method.
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https://hal.univ-cotedazur.fr/hal-01582605
Contributor : Richard Pasquetti <>
Submitted on : Wednesday, September 6, 2017 - 11:48:52 AM
Last modification on : Thursday, May 3, 2018 - 1:32:58 PM

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Richard Pasquetti. Spectral element schemes for the Korteweg-de Vries and Saint-Venant equations. 23ème Congrès Français de Mécanique (Mini-symposium Rencontres Mathématiques-Mécanique), Aug 2017, Lille, France. ⟨hal-01582605⟩

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