A finite difference method for the very weak solution to a Cauchy problem for an elliptic equation

A finite difference method for the very weak solution to a Cauchy problem for an elliptic equation Full article

Journal

Journal of Inverse and Ill-Posed Problems
ISSN: 0928-0219 , E-ISSN: 1569-3945

Output data

Year: 2018, Volume: 26, Number: 6, Pages: 835-857 Pages count : 23 DOI: 10.1515/jiip-2018-0060

Tags

Cauchy problem; elliptic equation; finite difference scheme; ill-posed problems; non-local boundary value problems; regularization; very weak solution

Authors

Hào D.N. ¹ , Thu Giang ² , Kabanikhin S. ^3,4,5 , Shishlenin M. ^3,4,5

Affiliations

1	Hanoi Institute of Mathematics, VAST, 18 Hoang Quoc Viet Road, Hanoi, Viet Nam
2	Thuongmai University, Ho Tung Mau, Hanoi, Viet Nam
3	Institute of Computational Mathematics and Mathematical Geophysics, 6 Lavrentieva Prospect, Novosibirsk, Russian Federation
4	Sobolev Institute of Mathematics, 4 Koptyuga Prospect, Novosibirsk, Russian Federation
5	Novosibirsk State University, 1 Pirogova str., Novosibirsk, Russian Federation

We introduce the concept of very weak solution to a Cauchy problem for elliptic equations. The Cauchy problem is regularized by a well-posed non-local boundary value problem whose solution is also understood in a very weak sense. A stable finite difference scheme is suggested for solving the non-local boundary value problem and then applied to stabilizing the Cauchy problem. Some numerical examples are presented for showing the efficiency of the method. © 2018 Walter de Gruyter GmbH, Berlin/Boston.

Hào D.N. , Thu G. , Kabanikhin S. , Shishlenin M.
A finite difference method for the very weak solution to a Cauchy problem for an elliptic equation
Journal of Inverse and Ill-Posed Problems. 2018. V.26. N6. P.835-857. DOI: 10.1515/jiip-2018-0060 WOS Scopus OpenAlex

Web of science:	WOS:000451640900008
Scopus:	2-s2.0-85055007477
OpenAlex:	W2897205603

DB	Citing
Scopus	10
OpenAlex	11
Web of science	7