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A Priori and a Posteriori Error Estimates for Boundary Control
Author: ChenRuiShan
Tutor: YangDanPing
School: East China Normal University
Course: Computational Mathematics
Keywords: constrained optimal control problem boundary control adaptive finite element method a priori error estimate a posteriori error estimate
CLC: O241.82
Type: Master's thesis
Year: 2010
Downloads: 31
Quote: 0
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Abstract
In this paper, we study adaptive finite element discretization schemes for an optimal control problem governed by elliptic PDE with a pointwise constraint for the control, with the constraints set K={u∈L2((?)Ω)u≥β}. We derive the firstorder optimality conditions from the boundary control problem. Finite element approximations are constructed on different meshes, which are suitable to treat different regularities of the control and state variables. A priori error estimates of optimal control for the finite element approximations are obtained. Furthmore, we derive the up and low bound of a posteriori error estimators for these approximations, which means that the estimators are efficient and reliable. Numerical experiments confirm our conclusions.

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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