A Prior Error Estimate for Linear Finite Element Approximation to Interface Optimal Control Problems

A Prior Error Estimate for Linear Finite Element Approximation to Interface Optimal Control Problems

This paper considers a linear finite element method for the constrained optimal control problems (OCPs) governed by elliptic interface equations. The state and adjoint state are approximated by the conforming P1 elements, while the control is approximated with the orthogonal projection of the adjoin...

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Veröffentlicht in:IAENG international journal of applied mathematics 2020-03, Vol.50 (1), p.1-6
Hauptverfasser: Guan, Hongbo, Hao, Chaoyang, Hong, Yapeng, Yin, Pei
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Elliptic functions
Finite element method
Mathematical analysis
Optimal control
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Zusammenfassung:This paper considers a linear finite element method for the constrained optimal control problems (OCPs) governed by elliptic interface equations. The state and adjoint state are approximated by the conforming P1 elements, while the control is approximated with the orthogonal projection of the adjoint state. Optimal order error estimates are proved in both L2-norm and broken energy norm. Lastly, some numerical results are presented to confirm the theoretical analysis.
ISSN:1992-9978
1992-9986