Local coderivatives and approximation of Hodge Laplace problems
Local coderivatives and approximation of Hodge Laplace problems
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Hodge Laplace 问题的局部编码导数和近似
DOI：
10.1090/mcom/3315
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
R. Winther
中科院分区：
文献类型：
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作者：
Jeonghun J. Lee;R. Winther
与de Rham复形相关的Hodge拉普拉斯问题的标准混合有限元近似是基于适当的离散子复形。因此，外导数，这是当地的运营商，计算准确。然而，相关的余导数的近似是非局部的。事实上，这种非局部属性是这些方法的混合制定的固有后果，并且可以被认为是这些计划的不期望的效果。因此，有人认为，至少在特殊情况下，更多的本地方法可能具有更好的属性。在本文中，我们构造这样的方法，依靠有限元空间的选择，自由度和数值积分规则之间的仔细平衡。此外，我们建立了关键的收敛估计的基础上，变分犯罪的标准方法。
The standard mixed finite element approximations of Hodge Laplace problems associated with the de Rham complex are based on proper discrete subcomplexes. As a consequence, the exterior derivatives, which are local operators, are computed exactly. However, the approximations of the associated coderivatives are nonlocal. In fact, this nonlocal property is an inherent consequence of the mixed formulation of these methods, and can be argued to be an undesired effect of these schemes. As a consequence, it has been argued, at least in special settings, that more local methods may have improved properties. In the present paper, we construct such methods by relying on a careful balance between the choice of finite element spaces, degrees of freedom, and numerical integration rules. Furthermore, we establish key convergence estimates based on a standard approach of variational crimes.
DOI：
10.1090/mcom/3354
发表时间：
2016-07
期刊：
Math. Comput.
影响因子：
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作者：
A. Gillette;Tyler Kloefkorn
通讯作者：
A. Gillette;Tyler Kloefkorn
一些最小有限元系统的构造
DOI：
10.1051/m2an/2015089
发表时间：
2016
期刊：
ESAIM: Mathematical Modelling and Numerical Analysis
影响因子：
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作者：
Christiansen, Snorre H.;Gillette, Andrew
通讯作者：
Gillette, Andrew