A quasi-boundary-value method for the Cauchy problem for elliptic equations with nonhomogeneous Neumann data
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
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.
Elliptic equation, a priori, a posteriori, discrete sine transform, finite difference method, quasi-boundary-value method, left-preconditioned GMRES
IdentifiersURN: urn:nbn:se:liu:diva-63347DOI: 10.1515/JIIP.2010.028ISI: 000285499000003OAI: oai:DiVA.org:liu-63347DiVA: diva2:378756