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 co-state 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 non-smooth 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.
Cite
@article{arxiv.2003.10474,
title = {Discontinuous Galerkin method for a distributed optimal control problem governed by a time fractional diffusion equation},
author = {Tao Wang and Binjie Li and Xiaoping Xie},
journal= {arXiv preprint arXiv:2003.10474},
year = {2020}
}