Analysis of the Scott–Zhang interpolation in the fractional order Sobolev spaces
Analysis of the Scott–Zhang interpolation in the fractional order Sobolev spaces
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分数阶 Sobolev 空间中的 Scott-Zhang 插值分析
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
P. Ciarlet
中科院分区：
文献类型：
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作者：
P. Ciarlet
Scott-Zhang插值算子自提出以来，一直受到人们的广泛关注。事实上，它拥有两个关键特征：它可以应用于没有逐点值的域，并且它保持边界条件。然而，在文献中似乎没有可用的逼近性能时，该领域的规则性是弱的。在本注记中，我们给出了在分数阶为0到1的Sobolev空间中测量的弱正则场的一些估计。
Abstract Since it was originally designed, the Scott-Zhang interpolation operator has been very popular. Indeed, it possesses two keys features: it can be applied to fields without pointwise values and it preserves the boundary condition. However, no approximability properties seem to be available in the literature when the regularity of the field is weak. In this Note, we provide some estimates for such weakly regular fields, measured in Sobolev spaces with fractional order between 0 and 1.