Analysis of a time-stepping discontinuous Galerkin method for modified anomalous subdiffusion problems

Abstract

This paper analyzes a time-stepping discontinuous Galerkin method for modified anomalous subdiffusion problems with two time fractional derivatives of orders $ α$ and $ β$ ($ 0 < α< β< 1 $). The stability of this method is established, the temporal accuracy of $ O(τ^{m+1-β/2}) $ is derived, where $m$ denotes the degree of polynomials for the temporal discretization. It is shown that, even the solution has singularity near $ t = {0+} $, this temporal accuracy can still be achieved by using the graded temporal grids. Numerical experiments are performed to verify the theoretical results.