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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Connections between the filtered discontinuous Galerkin method and the flux reconstruction approach to high order discretizations
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Connections between the filtered discontinuous Galerkin method and the flux reconstruction approach to high order discretizations

机译：滤波后的不连续Galerkin方法与通量重构方法之间的联系，以进行高阶离散化

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摘要

The purpose of this paper is to provide new insights on the connections that exist between the discontinuous Galerkin method (DG), the flux reconstruction method (FR) and the recently identified energy stable flux reconstruction method (ESFR) when solving time dependent conservation laws. All these schemes appear to be quite similar and it is important to understand how they are related. In this paper, we first review results on the stability of the discontinuous Galerkin method and extend it to the filtered discontinuous Galerkin method. We then consider the flux reconstruction approach and show its connections with DG. In particular, we show how the Energy Stable Flux Reconstruction method introduced by Vincent et al. is equivalent to a filtered DG method, hence giving a new proof of its stability. Also, it allows the use of the method without having to know the special form of the flux correction polynomials. Finally, we underline some fundamental differences that exist between FR and DG.
机译：本文的目的是提供新的见解，以解决不依赖时间的守恒定律时不连续的Galerkin方法（DG），通量重建方法（FR）和最近确定的能量稳定通量重建方法（ESFR）之间存在的联系。所有这些方案看起来都非常相似，因此了解它们之间的关系非常重要。在本文中，我们首先回顾了不连续Galerkin方法的稳定性，并将其扩展到过滤后的不连续Galerkin方法。然后，我们考虑通量重建方法并显示其与DG的联系。特别是，我们展示了Vincent等人介绍的能量稳定通量重建方法。等效于过滤的DG方法，因此提供了其稳定性的新证明。同样，它允许使用该方法而不必知道通量校正多项式的特殊形式。最后，我们强调了FR和DG之间存在的一些根本差异。

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