Abstract We consider the finite element approximation of fractional powers of regularly accretive operators via the Dunford–Taylor integral approach. We use a sinc quadrature scheme to approximate the Balakrishnan representation of the negative powers of the operator as well as its finite element approximation. We improve the exponentially convergent error estimates from [A. Bonito and J. E. Pasciak, IMA J. Numer. Anal., 37 (2016), No. 3, 1245–1273] by reducing the regularity required on the data. Numerical experiments illustrating the new theory are provided.

中文翻译：

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关于正增长算子的分数幂的Sinc正交逼近

摘要 我们通过 Dunford-Taylor 积分方法考虑了规则增殖算子的分数幂的有限元逼近。我们使用 sinc 正交方案来近似算子负幂的 Balakrishnan 表示及其有限元近似。我们改进了 [A. Bonito 和 JE Pasciak，IMA J. 数字。Anal., 37 (2016), No. 3, 1245–1273] 通过减少数据所需的规律性。提供了说明新理论的数值实验。