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

作　　者：Michel Bergmann Afaf Bouharguane Angelo Iollo Alexis Tardieu 

机构地区：[1]Centre Inria de l'Universite de Bordeaux,Memphis Team,Talence,France [2]Institut de Mathématiques de Bordeaux,UMR CNRS 5251,Talence,France [3]Universitéde Bordeaux,Bordeaux,France

出　　处：《Communications on Applied Mathematics and Computation》2024年第3期1954-1977,共24页应用数学与计算数学学报（英文）

摘　　要：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.

关 键 词：ADVECTION-DIFFUSION GALERKIN Arbitrary high order DERivatives(ADER)approach Interior Penalty Discontinuous Galerkin(IPDG) High-order schemes Empirical convergence rates 

分 类 号：O175[理学—数学]