Determination of a term in the right-hand side of parabolic equations

The inverse problem of determining a term in the right hand side of parabolic equations from integral observations is investigated. The observations can be regarded as generalized interior point observations which are collected in practice. The problem is then reformulated as a least squares problem...

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Published inJournal of computational and applied mathematics Vol. 309; pp. 28 - 43
Main Authors Hào, Dinh Nho, Huong, Bui Viet, Oanh, Nguyen Thi Ngoc, Thanh, Phan Xuan
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.01.2017
Subjects
Computational efficiency
Conjugate gradient method
Convergence
Coupling
Finite element method
Integral observations
Inverse problems
Inverse source problems
Least squares method
Mathematical analysis
Mathematical models
Tikhonov regularization
Finite element method
Conjugate gradient method
Inverse source problems
Least squares method
Tikhonov regularization
Integral observations
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Summary:The inverse problem of determining a term in the right hand side of parabolic equations from integral observations is investigated. The observations can be regarded as generalized interior point observations which are collected in practice. The problem is then reformulated as a least squares problem in coupling with a Tikhonov regularization term. It is proved that the Tikhonov functional is Fréchet differentiable and a formula for the gradient is derived via an adjoint problem. The variational problem is discretized by the finite element method, the convergence of which is proved. The discretized variational problem is numerically solved by the conjugate gradient method. Some numerical examples are presented for showing the efficiency of the method.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2016.05.022