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An iterative method for the Cauchy problem for second-order elliptic equations
Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten.
Ivan Franko Natl Univ Lviv, Ukraine.
Ivan Franko Natl Univ Lviv, Ukraine.
Aston Univ, England.ORCID-id: 0000-0001-9066-7922
Vise andre og tillknytning
2018 (engelsk)Inngår i: International Journal of Mechanical Sciences, ISSN 0020-7403, E-ISSN 1879-2162, Vol. 142, s. 216-223Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

The problem of reconstructing the solution to a second-order elliptic equation in a doubly-connected domain from knowledge of the solution and its normal derivative on the outer part of the boundary of the solution domain, that is from Cauchy data, is considered. An iterative method is given to generate a stable numerical approximation to this inverse ill-posed problem. The procedure is physically feasible in that boundary data is updated with data of the same type in the iterations, meaning that Dirichlet values is updated with Dirichlet values from the previous step and Neumann values by Neumann data. Proof of convergence and stability are given by showing that the proposed method is an extension of the Landweber method for an operator equation reformulation of the Cauchy problem. Connection with the alternating method is discussed. Numerical examples are included confirming the feasibility of the suggested approach.

sted, utgiver, år, opplag, sider
PERGAMON-ELSEVIER SCIENCE LTD , 2018. Vol. 142, s. 216-223
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Identifikatorer
URN: urn:nbn:se:liu:diva-149870DOI: 10.1016/j.ijmecsci.2018.04.042ISI: 000437372600019OAI: oai:DiVA.org:liu-149870DiVA, id: diva2:1236425
Tilgjengelig fra: 2018-08-02 Laget: 2018-08-02 Sist oppdatert: 2018-08-28

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