Bilinear Forms for the Recovery-Based Discontinuous Galerkin Method for Diffusion
Bilinear Forms for the Recovery-Based Discontinuous Galerkin Method for Diffusion
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发表时间：
2007
影响因子：
6
通讯作者：
M. V. Raalte;B. Leer
中科院分区：
文献类型：
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作者：
M. V. Raalte;B. Leer
本文介绍了双线性形式，相当于恢复为基础的不连续Galerkin制定的货车莱尔在2005年推出。的恢复方法近似的扩散方程的解在一个不连续的函数空间，而元件间的耦合是通过一个局部L2投影，恢复一个光滑的连续函数的基础上的不连续的近似。在这里，我们介绍了一个本地的“恢复多项式的基础”的概念-光滑的多项式，在弱意义上是不可区分的不连续的基础多项式-并显示它允许我们消除恢复过程。恢复方法再现对称的不连续Galerkin制定额外的惩罚一样的条款取决于该方法的目标精度。我们提出了唯一的恢复方法和间断Galerkin双线性形式之间的联系。
The present paper introduces bilinear forms that are equivalent to the recovery-based discontinuous Galerkin formulation introduced by Van Leer in 2005. The recovery method approximates the solution of the diffusion equation in a discontinuous function space, while inter-element coupling is achieved by a local L2 projection that recovers a smooth continuous function underlying the discontinuous approximation. Here we introduce the concept of a local “recovery polynomial basis” - smooth polynomials that are in the weak sense indistinguishable from the discontinuous basis polynomials - and show it allows us to eliminate the recovery procedure. The recovery method reproduces the symmetric discontinuous Galerkin formulation with additional penalty-like terms depending on the targeted accuracy of the method. We present the unique link between the recovery method and discontinuous Galerkin bilinear forms.