In this paper, a space–time spectral Galerkin method is revisited to address the multi-term time fractional diffusion equations. The proposed method is totally based on spectral method in both temporal and spatial discretization. A rigorous convergence analysis of the method is investigated. The main contribution of this work is to give an improved a posteriori error estimates for the spectral approximation. The validity and applicability of a posteriori error estimators are preformed by a numerical example, which verifies our theoretical claims.

中文翻译：

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多项式时间分数扩散方程的谱Galerkin方法的后验误差估计

在本文中，重新讨论了时空频谱Galerkin方法，以解决多项时间分数扩散方程。在时间和空间离散化方面，所提出的方法完全基于频谱方法。对该方法进行了严格的收敛分析。这项工作的主要贡献是为频谱近似提供了改进的后验误差估计。一个后验误差估计量的有效性和适用性是通过一个数值例子来进行的，该例子验证了我们的理论主张。