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Theoretical and numerical studies of the $P_NP_M$ DG schemes in one space dimension
Applications of Mathematics ( IF 0.7 ) Pub Date : 2019-11-20 , DOI: 10.21136/am.2019.0226-18
Abdulatif Badenjki , Gerald Warnecke

We give a proof of the existence of a solution of reconstruction operators used in the $P_NP_M$ DG schemes in one space dimension. Some properties and error estimates of the projection and reconstruction operators are presented. Then, by applying the $P_NP_M$ DG schemes to the linear advection equation, we study their stability obtaining maximal limits of the Courant numbers for several $P_NP_M$ DG schemes mostly experimentally. A numerical study explains how the stencils used in the reconstruction affect the efficiency of the schemes.

中文翻译:

一维空间中$P_NP_M$ DG 方案的理论和数值研究

我们证明了在一维空间中$P_NP_M$ DG 方案中使用的重构算子的解的存在性。介绍了投影和重建算子的一些属性和误差估计。然后,通过将$P_NP_M$ DG 方案应用于线性平流方程,我们主要通过实验研究它们的稳定性,以获得几个$P_NP_M$ DG 方案的Courant 数的最大极限。一项数值研究解释了重建中使用的模板如何影响方案的效率。
更新日期:2019-11-20
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