Explicit Upper Bounds for Dual Norms of Residuals
Explicit Upper Bounds for Dual Norms of Residuals
复制标题
残差对偶范数的显式上限
DOI：
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发表时间：
2009
影响因子：
2.9
通讯作者：
R. Verfürth
中科院分区：
文献类型：
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作者：
A. Veeser;R. Verfürth
我们导出了用局部庞加莱常数表示的显式残差对偶模的上界。残差是与有限元空间正交的连续线性泛函，其奇异部分支撑在底层网格的骨架上。这种类型的函数在后验误差估计中起关键作用。我们的主要工具是单位的离散划分、适当加权的迹和庞加莱不等式。对负一阶Sobolev范数和对流-反应-扩散问题中的对偶范数进行了说明。
We derive upper bounds for the dual norms of residuals that are explicit in terms of local Poincare constants. Residuals are continuous linear functionals that are orthogonal to a finite element space and have a singular part supported on the skeleton of the underlying mesh. Functionals of this type play a key role in a posteriori error estimation. Our main tools are a discrete partition of unity and suitably weighted trace and Poincare inequalities. The technique is illustrated for negative first order Sobolev norms and a dual norm arising in convection-reaction-diffusion problems.