Approximation of an elliptic control problem by the finite element method. (English) Zbl 0724.65069

Finite element approximations of an elliptic control problem are analyzed. Optimal order estimates are obtained in terms of the mesh size h and the target \(\Psi\). A computational scheme is derived which allows for the application of the conjugate gradient method. The scheme is implemented and tested on some model problems.


65K10 Numerical optimization and variational techniques
93C20 Control/observation systems governed by partial differential equations
Full Text: DOI


[1] DOI: 10.1090/S0025-5718-1986-0842125-3 · doi:10.1090/S0025-5718-1986-0842125-3
[2] DOI: 10.1016/0022-247X(73)90022-X · Zbl 0268.49036 · doi:10.1016/0022-247X(73)90022-X
[3] Geveci T., RAIRO Anal. Numer. 13 pp 313– (1979)
[4] Grisvard P., Elliptic Problems in Nonsmooth Domains (1985) · Zbl 0695.35060
[5] Groetsch C. W., The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind (1984) · Zbl 0545.65034
[6] DOI: 10.1137/0322029 · Zbl 0549.49024 · doi:10.1137/0322029
[7] Lions J. L., Non-Homogeneous Boundary Value Problems and Applications (1972) · Zbl 0223.35039
[8] Winther R., Ann. Mat. Pura Appl. 104 pp 73–
[9] DOI: 10.1137/0717002 · Zbl 0447.65021 · doi:10.1137/0717002
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