A posteriori error estimates of spectral Galerkin methods for multi-term time fractional diffusion equations

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.