Journal
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
Volume 61, Issue 1, Pages 135-158Publisher
SPRINGER
DOI: 10.1007/s10589-014-9700-x
Keywords
Convex optimal control; Integral constraint; A priori error estimate; A posteriori error estimator; Spectral method
Funding
- NSFC [11201212, 11301252]
- CSC [20140837045]
- Promotive Research Fund for Excellent Young and Middle-aged Scientists of Shandong Province [BS2012DX004]
- AMEP
- Special Funds for Doctoral Authorities of Linyi University
- [LYDX2013BS054]
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In this paper, we investigate the optimal control problems governed by elliptic equations with integral constraint for state variable in one dimension by Legendre-Galerkin spectral methods. We deduce optimal conditions of the optimal control problems. Meanwhile, we obtain an a priori error estimate and a posteriori error estimator. Furthermore, we obtain an explicit formula of the a posteriori error estimator by orthogonal properties of Legendre polynomials. Finally, we present numerical examples to confirm our analytical results.
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