BERGMANN, Michel; BOUHARGUANE, Afaf; IOLLO, Angelo; TARDIEU, Alexis

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BERGMANN, Michel
Institut de Mathématiques de Bordeaux [IMB]
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]

BOUHARGUANE, Afaf
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]
Institut de Mathématiques de Bordeaux [IMB]
Université de Bordeaux [UB]

IOLLO, Angelo
Institut de Mathématiques de Bordeaux [IMB]
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]

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Document de travail - Pré-publication

Résumé en anglais

We present a high-order Galerkin method in both space and time for the one-dimensional unsteady advectiondiffusion equation. Three Interior Penalty Discontinuous Galerkin (IPDG) schemes are detailed for the space discretization, while the time integration is performed at the same order of accuracy thanks to an Arbitrary high order DERivatives (ADER) method. The orders of convergence of the three ADER-IPDG methods are carefully examined through numerical illustrations, showing that the approach is consistent, accurate and efficient.The numerical results indicate that the symmetric version of IPDG is typically more accurate and more ecient compared to the other approaches.< Réduire

Mots clés en anglais

Advection-diffusion

Galerkin

ADER approach

IPDG

high-order schemes

empirical convergence rates

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High order ADER-IPDG methods for the unsteady advection-diffusion equation

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Résumé en anglais

Mots clés en anglais

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