On the Quadrature and Weak Form Choices in Collocation Type Discontinuous Galerkin Spectral Element Methods
On the Quadrature and Weak Form Choices in Collocation Type Discontinuous Galerkin Spectral Element Methods
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DOI：
10.1007/s10915-010-9372-3
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发表时间：
2010-08
影响因子：
2.5
通讯作者：
D. Kopriva;G. Gassner
中科院分区：
文献类型：
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作者：
D. Kopriva;G. Gassner
我们研究了四边形或六面体网格守恒定律系统的张量积不连续伽辽金谱元近似的四个节点版本。它们源自高斯求积或高斯-洛巴托求积的两种选择，并按不连续伽辽金方法的一次 (I) 或两次 (II) 公式进行积分。我们证明，当使用全局多项式插值来近似单元内的解和通量时，这两个公式实际上在代数上与高斯或高斯-洛巴托求积等效。数值实验证实了近似值的等价性，并表明使用高斯求积和分部积分一次是四种近似值中最有效的。
We examine four nodal versions of tensor product discontinuous Galerkin spectral element approximations to systems of conservation laws for quadrilateral or hexahedral meshes. They arise from the two choices of Gauss or Gauss-Lobatto quadrature and integrate by parts once (I) or twice (II) formulations of the discontinuous Galerkin method. We show that the two formulations are in fact algebraically equivalent with either Gauss or Gauss-Lobatto quadratures when global polynomial interpolations are used to approximate the solutions and fluxes within the elements. Numerical experiments confirm the equivalence of the approximations and indicate that using Gauss quadrature with integration by parts once is the most efficient of the four approximations.