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A quasi-boundary-value method for the Cauchy problem for elliptic equations with  nonhomogeneous Neumann data
Lanzhou University.
Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap. Linköpings universitet, Tekniska högskolan.ORCID-id: 0000-0003-2281-856X
Lanzhou University.
2010 (engelsk)Inngår i: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 18, nr 6, s. 617-645Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

A Cauchy problem for elliptic equations with nonhomogeneous Neumann datain a cylindrical domain is investigated in this paper. For the theoretical aspect the a-prioriand a-posteriori parameter choice rules are suggested and the corresponding error estimatesare obtained. About the numerical aspect, for a simple case results given by twomethods based on the discrete Sine transform and the finite difference method are presented;an idea of left-preconditioned GMRES (Generalized Minimum Residual) methodis proposed to deal with the high dimensional case to save the time; a view of dealingwith a general domain is suggested. Some ill-posed problems regularized by the quasiboundary-value method are listed and some rules of this method are suggested.

sted, utgiver, år, opplag, sider
Walter de Gruyter , 2010. Vol. 18, nr 6, s. 617-645
Emneord [en]
Elliptic equation, a priori, a posteriori, discrete sine transform, finite difference method, quasi-boundary-value method, left-preconditioned GMRES
HSV kategori
Identifikatorer
URN: urn:nbn:se:liu:diva-63347DOI: 10.1515/JIIP.2010.028ISI: 000285499000003OAI: oai:DiVA.org:liu-63347DiVA, id: diva2:378756
Tilgjengelig fra: 2010-12-16 Laget: 2010-12-16 Sist oppdatert: 2017-12-11

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