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Journal of Scientific Computing

Erschienen in:

05.06.2015

A Stabilized Mixed Finite Element Method for Elliptic Optimal Control Problems

verfasst von: Hongfei Fu, Hongxing Rui, Jian Hou, Haihong Li

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2016

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Abstract

In this paper, we propose a new mixed finite element method, called stabilized mixed finite element method, for the approximation of optimal control problems constrained by a first-order elliptic system. This method is obtained by adding suitable elementwise least-squares residual terms for the primal state variable y and its flux \(\sigma \). We prove the coercive and continuous properties for the new mixed bilinear formulation at both continuous and discrete levels. Therefore, the finite element function spaces do not require to satisfy the Ladyzhenkaya–Babuska–Brezzi consistency condition. Furthermore, the state and flux state variables can be approximated by the standard Lagrange finite element. We derive optimality conditions for such optimal control problems under the concept of Discretization-then-Optimization, and then a priori error estimates in a weighted norm are discussed. Finally, numerical experiments are given to confirm the efficiency and reliability of the stabilized method.

Vorheriger Artikel Finite Element Method and A Priori Error Estimates for Dirichlet Boundary Control Problems Governed by Parabolic PDEs

Nächster Artikel Erratum to: A Stabilized Mixed Finite Element Method for Elliptic Optimal Control Problems

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Titel: A Stabilized Mixed Finite Element Method for Elliptic Optimal Control Problems
verfasst von: Hongfei Fu
Hongxing Rui
Jian Hou
Haihong Li
Publikationsdatum: 05.06.2015
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-015-0050-3

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