Communications on Applied Mathematics and Computation >

2024 , Vol. 6 >Issue 3: 1954 - 1977

DOI: https://doi.org/10.1007/s42967-023-00355-w

ORIGINAL PAPERS

High Order ADER-IPDG Methods for the Unsteady Advection-Diffusion Equation

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  • 1 Centre Inria de l'Université de Bordeaux, Memphis Team, Talence, France;
    2 Institut de Mathématiques de Bordeaux, UMR CNRS 5251, Talence, France;
    3 Université de Bordeaux, Bordeaux, France

Received date: 2023-02-25

  Revised date: 2023-09-19

  Accepted date: 2023-11-28

  Online published: 2024-12-20

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Abstract

We present a high-order Galerkin method in both space and time for the 1D unsteady linear advection-diffusion 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 efficient compared to the other approaches.

Key words： Advection-diffusion; Galerkin; Arbitrary high order DERivatives (ADER) approach; Interior Penalty Discontinuous Galerkin (IPDG); High-order schemes; Empirical convergence rates

Cite this article

Michel Bergmann, Afaf Bouharguane, Angelo Iollo, Alexis Tardieu . High Order ADER-IPDG Methods for the Unsteady Advection-Diffusion Equation[J]. Communications on Applied Mathematics and Computation, 2024 , 6(3) : 1954 -1977 . DOI: 10.1007/s42967-023-00355-w

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