French, Donald A.; King, J. Thomas Approximation of an elliptic control problem by the finite element method. (English) Zbl 0724.65069 Numer. Funct. Anal. Optimization 12, No. 3-4, 299-314 (1991). 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. Reviewer: D.A.French (Cincinnati, OH) Cited in 36 Documents MSC: 65K10 Numerical optimization and variational techniques 93C20 Control/observation systems governed by partial differential equations Keywords:numerical examples; Finite element; elliptic control problem; Optimal order estimates; conjugate gradient method PDF BibTeX XML Cite \textit{D. A. French} and \textit{J. T. King}, Numer. Funct. Anal. Optim. 12, No. 3--4, 299--314 (1991; Zbl 0724.65069) Full Text: DOI OpenURL References: [1] DOI: 10.1090/S0025-5718-1986-0842125-3 [2] DOI: 10.1016/0022-247X(73)90022-X · Zbl 0268.49036 [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 [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.