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

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A finite difference method for the very weak solution to a Cauchy problem for an elliptic equation. / Hào, Dinh Nho; Thu Giang, Le Thi; Kabanikhin, Sergey et al.

In: Journal of Inverse and Ill-Posed Problems, Vol. 26, No. 6, 01.12.2018, p. 835-857.

Research output: Contribution to journal › Article › peer-review

Author

Hào, Dinh Nho ; Thu Giang, Le Thi ; Kabanikhin, Sergey et al. / A finite difference method for the very weak solution to a Cauchy problem for an elliptic equation. In: Journal of Inverse and Ill-Posed Problems. 2018 ; Vol. 26, No. 6. pp. 835-857.

BibTeX

@article{db12b12ee9b74c5d9fbb3f14aae4570e,

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

abstract = "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.",

keywords = "Cauchy problem, elliptic equation, finite difference scheme, ill-posed problems, non-local boundary value problems, regularization, very weak solution, INVERSE",

author = "H{\`a}o, {Dinh Nho} and {Thu Giang}, {Le Thi} and Sergey Kabanikhin and Maxim Shishlenin",

year = "2018",

month = dec,

day = "1",

doi = "10.1515/jiip-2018-0060",

language = "English",

volume = "26",

pages = "835--857",

journal = "Journal of Inverse and Ill-Posed Problems",

issn = "0928-0219",

publisher = "Walter de Gruyter GmbH",

number = "6",

}

RIS

TY - JOUR

T1 - A finite difference method for the very weak solution to a Cauchy problem for an elliptic equation

AU - Hào, Dinh Nho

AU - Thu Giang, Le Thi

AU - Kabanikhin, Sergey

AU - Shishlenin, Maxim

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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.

AB - 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.

KW - Cauchy problem

KW - elliptic equation

KW - finite difference scheme

KW - ill-posed problems

KW - non-local boundary value problems

KW - regularization

KW - very weak solution

KW - INVERSE

UR - http://www.scopus.com/inward/record.url?scp=85055007477&partnerID=8YFLogxK

U2 - 10.1515/jiip-2018-0060

DO - 10.1515/jiip-2018-0060

M3 - Article

AN - SCOPUS:85055007477

VL - 26

SP - 835

EP - 857

JO - Journal of Inverse and Ill-Posed Problems

JF - Journal of Inverse and Ill-Posed Problems

SN - 0928-0219

IS - 6

ER -

ID: 17141561