A posteriori error estimates of spectral Galerkin methods for multi-term time fractional diffusion equations. (October 2021)

• Record Type: Journal Article
• Authors: Tang, Bo; Chen, Yanping; Lin, Xiuxiu
• Is Part Of: Applied mathematics letters. Volume 120(2021)
• Publication Date: 2021-10
• Subjects: Spectral Galerkin methods -- Fractional diffusion equations -- A posteriori error estimates; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107259
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: 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.