Functional a posteriori error estimates for discontinuous Galerkin approximations of elliptic problems
Functional a posteriori error estimates for discontinuous Galerkin approximations of elliptic problems
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椭圆问题的不连续伽辽金近似的函数后验误差估计
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
S. Tomar
中科院分区：
文献类型：
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作者：
R. Lazarov;S. Repin;S. Tomar
在本文中，我们开发了椭圆边值问题的不连续伽辽金近似的泛函后验误差估计。这些估计是基于DG近似对各自能量空间的一定投影和S. Repin开发的符合近似的函数后验估计（例如，Math Comp 69(2000) 481-500）。在此基础上，我们导出了“破能”范数误差的双面保证可计算界。给出的一系列数值算例证实了估计的有效性。©2008 Wiley期刊公司数值方法偏微分方程，2009
In this article, we develop functional a posteriori error estimates for discontinuous Galerkin (DG) approximations of elliptic boundary‐value problems. These estimates are based on a certain projection of DG approximations to the respective energy space and functional a posteriori estimates for conforming approximations developed by S. Repin (see e.g., Math Comp 69 (2000) 481–500). On these grounds, we derive two‐sided guaranteed and computable bounds for the errors in “broken” energy norms. A series of numerical examples presented confirm the efficiency of the estimates. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009