A discontinuous finite volume element method for second‐order elliptic problems
A discontinuous finite volume element method for second‐order elliptic problems
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DOI：
10.1002/num.20626
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发表时间：
2012-03
影响因子：
3.9
通讯作者：
C. Bi;Ming Liu
中科院分区：
文献类型：
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作者：
C. Bi;Ming Liu
本文提出了求解二阶椭圆型问题的一种新的不连续有限体积元（DFVE）方法。我们将DFVE方法视为内罚方法的扰动，并在网格依赖范数中得到DFVE方法解与内罚方法解之间的超逼近估计。这表明DFVE方法比我们所知道的更接近于内部处罚方法。利用这种超逼近估计，我们可以很容易地得到DFVE方法的L2 -范数和最大范数的最优阶误差估计。©2010 Wiley期刊公司数值方法偏微分方程28:425-440,2012
In this article, we propose a new discontinuous finite volume element (DFVE) method for the second‐order elliptic problems. We treat the DFVE method as a perturbation of the interior penalty method and get a superapproximation estimate in a mesh dependent norm between the solution of the DFVE method and that of the interior penalty method. This reveals that the DFVE method is much closer to the interior penalty method than we have known. By using this superapproximation estimate, we can easily get the optimal order error estimates in the L2 ‐norm and in the maximum norms of the DFVE method.© 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 425–440, 2012