Discontinuous Galerkin method for a distributed optimal control problem governed by a time fractional diffusion equation

This paper is devoted to the numerical analysis of a control constrained distributed optimal problem subject time fractional diffusion equation with non-smooth initial data. The solutions state and co-state are decomposed into singular regular parts, some growth estimates obtained for parts. Following variational discretization concept, full applied corresponding equations by using linear conforming finite element method in space piecewise constant discontinuous Galerkin time. By estimates, error derived In particular, graded temporal grids used obtain first-order accuracy. Finally, experiments performed verify theoretical results.