Geodesic
Numerical solution of the inverse Cauchy problem for the elliptic equation
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 308-316

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This paper is interested at the Cauchy problem for Laplace's equation, which is to recover Dirichlet condition on the accessible part of the domain from additional conditions on the other part of domain. To solve this kind of ill-posed problem, we use a variational iterative method. Also, a direct method for numerical solution of the inverse boundary value problem is presented.
Keywords: inverse problem, ill-posed problem, iterative method, direct method, difference scheme.
Mots-clés : Laplace equation 
@article{SEMR_2017_14_a104,
     author = {G. A. Prokopev and V. I. Vasil'ev and A. M. Kardashevsky and P. V. Sivsev},
     title = {Numerical solution of the inverse {Cauchy} problem for the elliptic equation},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {308--316},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a104/}
}
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G. A. Prokopev; V. I. Vasil'ev; A. M. Kardashevsky; P. V. Sivsev. Numerical solution of the inverse Cauchy problem for the elliptic equation. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 308-316. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a104/