@article{Choi2022, 
author = {Woocheol Choi and Young-Pil Choi},
title = {A sharp error analysis for the DG method of optimal control problems},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {5},
pages = {9117-9155},
keywords = {optimal control problem, discontinuous Galerkin method},
url = {https://www.sciopen.com/article/10.3934/math.2022506},
doi = {10.3934/math.2022506},
abstract = {In this paper, we are concerned with a nonlinear optimal control problem of ordinary differential equations. We consider a discretization of the problem with the discontinuous Galerkin method with arbitrary order    r  ∈      N    ∪  {  0  }. Under suitable regularity assumptions on the cost functional and solutions of the state equations, we first show the existence of a local solution to the discretized problem. We then provide sharp estimates for the        L    2  -error of the approximate solutions. The convergence rate of the error depends on the regularity of the optimal solution              u      ¯       and its adjoint state with the degree of piecewise polynomials. Numerical experiments are presented supporting the theoretical results.}
}