6533b874fe1ef96bd12d5ffb
RESEARCH PRODUCT
Discretization estimates for an elliptic control problem
Viorel ArnǎutuPekka Neittaanmäkisubject
Control and OptimizationPartial differential equationDiscretizationMathematical analysisOptimal controlFinite element methodComputer Science ApplicationsElliptic curveSignal ProcessingCalculus of variationsSpectral methodAnalysisMathematicsDiscretization of continuous featuresdescription
An optimal control problem governed by an elliptic equation written in variational form in an abstract functional framework is considered. The control is subject to restrictions. The optimality conditions are established and the Ritz-Galerkin discretization is introduced. If the error estimate corresponding to the elliptic equation is given as a function like where h is the discretization parameter and is an integer, then the error estimates for the optimal control, for the optimal state and for the optimal value are obtained. These results are applied first for a Two-Point BVP and next for a 2D/3D elliptic problem as state equation. Next a spectral method is used in the discretization process. The estimates obtained in the abstract case are applied to a distributed control problem and to a boundary control problem.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1998-01-01 | Numerical Functional Analysis and Optimization |