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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 18, Issue 6 (Jan 2010)


A quasi-boundary-value method for the Cauchy problem for elliptic equations with nonhomogeneous Neumann data

Xiao-Li Feng
  • School of Mathematics and Statistics, Lanzhou University, Lanzhou, P.R. China and Department of Mathematics, Linköping University, Sweden.
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/ Lars Eldén / Chu-Li Fu
Published Online: 2010-12-20 | DOI: https://doi.org/10.1515/jiip.2010.028


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

Keywords.: Elliptic equation; a-priori; a-posteriori; discrete Sine transform; finite difference method; quasi-boundary-value method; left-preconditioned GMRES

About the article

Received: 2010-03-26

Published Online: 2010-12-20

Published in Print: 2010-12-01

Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2010.028.

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