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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 first-order optimality condi-tions 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 estima-tors 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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