| Autor: |
Woocheol Choi, Young-Pil Choi |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
AIMS Mathematics, Vol 7, Iss 5, Pp 9117-9155 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.2022506?viewType=HTML |
| Popis: |
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 \in \mathbb{N}\cup \{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 $ \bar{u} $ and its adjoint state with the degree of piecewise polynomials. Numerical experiments are presented supporting the theoretical results. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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