ALTERNATING METHOD FOR SOLVING A BIHARMONIC INVERSE PROBLEM IN DETECTION OF ROBIN COEFFICIENTS

In this paper, we are interested in an inverse problem of detection of corrosion for a biharmonic equation which consists to determine the Robin coefficients in the inaccessible part of the boundary from the Riquiert-Neumann data on the accessible one. For this end, we consider the factorisation of...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 13; no. 4; p. 1605
Main Authors Jouilik, B, Daoudi, J, Tajani, C, Abouchabaka, J
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.01.2023
Elman Hasanoglu
Subjects
Algorithms
Biharmonic equations
Boundary conditions
Cauchy problems
Finite element analysis
Inverse problems
Iterative methods
Methods
Missing data
Poisson equation
Morocco
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ISSN2146-1147
2146-1147

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Summary:In this paper, we are interested in an inverse problem of detection of corrosion for a biharmonic equation which consists to determine the Robin coefficients in the inaccessible part of the boundary from the Riquiert-Neumann data on the accessible one. For this end, we consider the factorisation of the biharmonic problem which gives rise to two Cauchy problems for Laplace and Poisson equations. An algorithm based on an alternative iterative method is proposed allowing to complete the missing Cauchy data and then recover the Robin coefficients. We show the feasibility of this approach by numerical reconstructions. Keywords: ill-posed problem, inverse problem, biharmonic equation, finite element method. AMS Subject Classification: 65N21, 35J05, 31A30.
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ISSN:2146-1147
2146-1147