An Improved Finite Element Approximation and Superconvergence for Temperature Control Problems

In this paper, we consider an improved finite element approximation for temperature control problems, where the state and the adjoint state are discretized by piecewise linear functions while the control is not discretized directly. The numerical solution of the control is obtained by a projection o...

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Bibliographic Details
Published inMathematical modelling and analysis Vol. 18; no. 5; pp. 631 - 640
Main Author Tang, Yuelong
Format Journal Article
LanguageEnglish
Published Taylor & Francis 01.12.2013
Vilnius Gediminas Technical University
Subjects
Adjoints
approximation
convergence analysis
finite element method
optimal control
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Summary:In this paper, we consider an improved finite element approximation for temperature control problems, where the state and the adjoint state are discretized by piecewise linear functions while the control is not discretized directly. The numerical solution of the control is obtained by a projection of the adjoint state to the set of admissible controls. We derive a priori error estimates and superconvergence of second-order. Moreover, we present some numerical examples to illustrate our theoretical results.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1392-6292
1648-3510
DOI:10.3846/13926292.2013.868840