Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods
Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods
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DOI：
10.4208/jcm.2003-m2018-0223
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发表时间：
2018-05
影响因子：
0.9
通讯作者：
Q. Hong;Jinchao Xu
中科院分区：
文献类型：
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作者：
Q. Hong;Jinchao Xu
在本文中，我们对混合间断伽辽金（HDG）和弱伽辽金（WG）方法的稳定性和收敛性提供了一些新的估计。通过使用混合方法的标准 Brezzi 理论，我们仔细地为各种离散化变量定义适当的范数，然后确定稳定性和误差估计对于稳定性和离散化参数保持一致。因此，通过对稳定参数进行适当的限制，我们表明 HDG 方法收敛于原始一致方法，WG 方法收敛于混合一致方法。
In this paper, we provide a number of new estimates on the stability and convergence of both hybrid discontinuous Galerkin (HDG) and weak Galerkin (WG) methods. By using the standard Brezzi theory on mixed methods, we carefully define appropriate norms for the various discretization variables and then establish that the stability and error estimates hold uniformly with respect to stabilization and discretization parameters. As a result, by taking appropriate limit of the stabilization parameters, we show that the HDG method converges to a primal conforming method and the WG method converge to a mixed conforming method.