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Superconvergence of Finite Method for Optimal Control Problems Governed by Parabolic Equations

Author: ZouYanHua
Tutor: ChenYanPing
School: Xiangtan University
Course: Computational Mathematics
Keywords: Finite Element Approximation Superconvergence Parabolic equation Optimal control problem
CLC: O241.82
Type: Master's thesis
Year: 2008
Downloads: 24
Quote: 0
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Abstract


The optimal control problem is very important for many engineering applications . In the past few decades , the optimal control problem is a very active and a very successful field . Obviously , an effective numerical method is successfully solve the crux of the issue of the optimal control . Finite element approximation method to solve the optimal control problem plays a very important role . In this paper , we study the state equation for optimal control problems for linear parabolic equations , some SUPERCONVERGENCE obtained by use of the finite element approximation . Where the state variables and the dual state variable is a linear function of the slice to approximate the control variables using piecewise constant functions to approximate . We will first establish the optimal control problem approximation format , then the introduction and derive some intermediate variable error estimates , its conclusion , we will get the results on Superconvergence analysis of control and status variables .

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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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