Error analysis of discontinuous Galerkin finite element method for optimal control problem governed by the transport equation |
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| Authors: | Huipo Liu Shuanghu Wang Hongbin Han Lan Yuan |
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| Affiliation: | 1. Institute of Applied Physics and Computational Mathematics, Beijing, China;2. Department of Radiology, Peking University Third Hospital, Peking University, Beijing, China;3. Beijing Key Lab of Magnetic Resonance Imaging Technology, Beijing, China;4. Center of Medical and Health Analysis, Peking University, Beijing, China |
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| Abstract: | This article discusses a priori and a posteriori error estimates of discontinuous Galerkin finite element method for optimal control problem governed by the transport equation. We use variational discretization concept to discretize the control variable and discontinuous piecewise linear finite elements to approximate the state and costate variable. Based on the error estimates of discontinuous Galerkin finite element method for the transport equation, we get a priori and a posteriori error estimates for the transport equation optimal control problem. Finally, two numerical experiments are carried out to confirm the theoretical analysis.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1493–1512, 2017 |
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| Keywords: | a posteriori error estimate a priori error estimate discontinuous Galerkin finite element method optimal control transport equation |
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