A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation
A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation
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DOI：
10.1137/060665993
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发表时间：
2007-06
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影响因子：
--
通讯作者：
M. Ainsworth
中科院分区：
文献类型：
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作者：
M. Ainsworth
本文证明了间断伽辽金有限元逼近中的单元间间断从属于间断H^1 $-间断的测量误差。一个推论是误差的DG范数等价于断裂能量范数。可计算的后验误差界获得的DG-范数和破碎的能量的误差测量，并被证明是有效的，在这个意义上，他们也提供了一个常数和高阶数据振荡项的下限。估计是完全免费的未知常数，并提供保证的数值界的错误。
It is shown that the interelement discontinuities in a discontinuous Galerkin finite element approximation are subordinate to the error measured in the broken $H^1$-seminorm. One consequence is that the DG-norm of the error is equivalent to the broken energy seminorm. Computable a posteriori error bounds are obtained for the error measured in both the DG-norm and the broken energy seminorm and are shown to be efficient in the sense that they also provide lower bounds up to a constant and higher order data oscillation terms. The estimators are completely free of unknown constants and provide guaranteed numerical bounds for the error.