TY  - JOUR
AU  - Choi, Woocheol
AU  - Choi, Young-Pil
PY  - 2022
TI  - A sharp error analysis for the DG method of optimal control problems
JO  - AIMS Mathematics
SP  - 9117
EP  - 9155
VL  - 7
IS  - 5
AB  - 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.
UR  - https://doi.org/10.3934/math.2022506
DO  - 10.3934/math.2022506