This paper is devoted to the error analysis of a time-spectral algorithm for fractional diffusion problems of order $\alpha$ ($0 < \alpha < 1$). The solution regularity in the Sobolev space is revisited, and new regularity results in the Besov space are established. A time-spectral algorithm is developed which adopts a standard spectral method and a conforming linear finite element method for temporal and spatial discretizations, respectively. Optimal error estimates are derived with nonsmooth data. Particularly, a sharp temporal convergence rate $1+2\alpha$ is shown theoretically and numerically.

翻译：本文专门论述对时间光谱算法的错误分析,该算法用于分析单位扩散问题($\alpha$(0 < αpha < 1美元))的分位扩散问题。索博列夫空间的溶解规律性得到重新审视,贝索夫空间的新的规律性结果得到确定。开发了时间光谱算法,分别采用标准光谱法和符合的线性有限元素法,用于时间和空间分解。最佳误差估计是用非光学数据得出的。特别是,从理论上和数字上显示了急剧的时间趋同率1+2\阿尔法元。