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A quasi-boundary-value method for the Cauchy problem for elliptic equations with  nonhomogeneous Neumann data
Lanzhou University.
Linköping University, Department of Mathematics, Scientific Computing. Linköping University, The Institute of Technology.ORCID iD: 0000-0003-2281-856X
Lanzhou University.
2010 (English)In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 18, no 6, 617-645 p.Article in journal (Refereed) 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.

Place, publisher, year, edition, pages
Walter de Gruyter , 2010. Vol. 18, no 6, 617-645 p.
Keyword [en]
Elliptic equation, a priori, a posteriori, discrete sine transform, finite difference method, quasi-boundary-value method, left-preconditioned GMRES
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-63347DOI: 10.1515/JIIP.2010.028ISI: 000285499000003OAI: diva2:378756
Available from: 2010-12-16 Created: 2010-12-16 Last updated: 2014-09-23

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