首页|High Order ADER-IPDG Methods for the Unsteady Advection-Diffusion Equation
High Order ADER-IPDG Methods for the Unsteady Advection-Diffusion Equation
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We present a high-order Galerkin method in both space and time for the 1D unsteady lin-ear 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 exam-ined 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.
Advection-diffusionGalerkinArbitrary high order DERivatives(ADER)approachInterior Penalty Discontinuous Galerkin(IPDG)High-order schemesEmpirical convergence rates
Michel Bergmann、Afaf Bouharguane、Angelo Iollo、Alexis Tardieu
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Centre Inria de l'Université de Bordeaux,Memphis Team,Talence,France
Institut de Mathématiques de Bordeaux,UMR CNRS 5251,Talence,France
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