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

Abstract

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

Fractional spectral collocation method for optimal control problem governed by space fractional diffusion equation

“…Various numerical methods have been investigated for the optimal control problems with FDE constraints, e.g. finite element methods [4,5,10,17,23,33,38,39,41], spectral Galerkin methods [32,34,35,40], collocation methods [25,26,36], etc.…”