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Journal of Scientific Computing

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21-09-2018

Finite Element Approximation of Optimal Control Problem Governed by Space Fractional Equation

Authors: Zhaojie Zhou, Zhiyu Tan

Published in: Journal of Scientific Computing | Issue 3/2019

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Abstract

In this paper we investigate finite element approximation of optimal control problem governed by space fractional diffusion equation with control constraints. The control variable is approximated by piecewise constant. Regularity estimate for the control problem is proved based on the first order optimality system and a priori error estimates for the state, the adjoint state and the control variables are derived. Due to the nonlocal property of fractional derivative, which will leads to a full stiff matrix, we develop a fast primal dual active set algorithm for the control problem. Numerical examples are given to illustrate the theoretical findings and the efficiency of the fast algorithm.

previous article Positivity-Preserving Time Discretizations for Production–Destruction Equations with Applications to Non-equilibrium Flows

next article Error Analysis of a Fully Discrete Morley Finite Element Approximation for the Cahn–Hilliard Equation

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Title: Finite Element Approximation of Optimal Control Problem Governed by Space Fractional Equation
Authors: Zhaojie Zhou
Zhiyu Tan
Publication date: 21-09-2018
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 3/2019
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-018-0829-0

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