Convergence and superconvergence of variational discretization for parabolic bilinear optimization problems

In this paper, we investigate a variational discretization approximation of parabolic bilinear optimal control problems with control constraints. For the state and co-state variables, triangular linear finite element and difference methods are used for space and time discretization, respectively, su...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2019; no. 1; pp. 1 - 13
Main Authors Tang, Yuelong, Hua, Yuchun
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 06.09.2019
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Bilinear optimal control
Convergence
Discretization
Economic models
Mathematics
Mathematics and Statistics
Optimal control
Optimization
State variable
Superconvergence
Variational discretization
Superconvergence
65M60
Variational discretization
49J20
Bilinear optimal control
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Summary:In this paper, we investigate a variational discretization approximation of parabolic bilinear optimal control problems with control constraints. For the state and co-state variables, triangular linear finite element and difference methods are used for space and time discretization, respectively, superconvergence in H 1 -norm between the numerical solutions and elliptic projections are derived. Although the control variable is not discrete directly, convergence of second order in L 2 -norm is obtained. These theoretical results are confirmed by two numerical examples.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-019-2195-3