Error estimation of a discontinuous Galerkin method for time fractional subdiffusion problems with nonsmooth data

TL;DR

This paper analyzes a discontinuous Galerkin method for time fractional subdiffusion problems with nonsmooth data, establishing regularity, deriving optimal error estimates, and verifying results through numerical experiments.

Contribution

It provides the first comprehensive error analysis of a DG method for subdiffusion problems with low regularity data.

Findings

Optimal error estimates are derived for nonsmooth data.

Numerical experiments confirm theoretical error bounds.

Regularity of solutions is established using variational methods.

Abstract

This paper is devoted to the numerical analysis of a piecewise constant discontinuous Galerkin method for time fractional subdiffusion problems. The regularity of weak solution is firstly established by using variational approach and Mittag-Leffler function. Then several optimal error estimates are derived with low regularity data. Finally, numerical experiments are conducted to verify the theoretical results.