Standard

Solving the Pure Neumann Problem by a Finite Element Method. / Ivanov, M. I.; Kremer, I. A.; Urev, M. V.

In: Numerical Analysis and Applications, Vol. 12, No. 4, 01.10.2019, p. 359-371.

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

Harvard

Ivanov, MI, Kremer, IA & Urev, MV 2019, 'Solving the Pure Neumann Problem by a Finite Element Method', Numerical Analysis and Applications, vol. 12, no. 4, pp. 359-371. https://doi.org/10.1134/S1995423919040049

APA

Ivanov, M. I., Kremer, I. A., & Urev, M. V. (2019). Solving the Pure Neumann Problem by a Finite Element Method. Numerical Analysis and Applications, 12(4), 359-371. https://doi.org/10.1134/S1995423919040049

Vancouver

Ivanov MI, Kremer IA, Urev MV. Solving the Pure Neumann Problem by a Finite Element Method. Numerical Analysis and Applications. 2019 Oct 1;12(4):359-371. doi: 10.1134/S1995423919040049

Author

Ivanov, M. I. ; Kremer, I. A. ; Urev, M. V. / Solving the Pure Neumann Problem by a Finite Element Method. In: Numerical Analysis and Applications. 2019 ; Vol. 12, No. 4. pp. 359-371.

BibTeX

@article{8fce86d313ea4c55b95e7a4e937b2af6,
title = "Solving the Pure Neumann Problem by a Finite Element Method",
abstract = "This paper deals with the solution of the pure Neumann problem for the diffusion equation by a finite element method. First, an extended generalized formulation of the Neumann problem in the Sobolev space H1(Ω) is derived and investigated. Then a discrete analog of this problem is formulated by using standard finite element approximations of the space H1(Ω). An iterative method for solving the corresponding SLAE is proposed. Some examples of solving model problems are used to discuss the numerical properties of the algorithm proposed.",
keywords = "consistency conditions, finite elements, orthogonalization of the right-hand side, pure Neumann problem, APPROXIMATION",
author = "Ivanov, {M. I.} and Kremer, {I. A.} and Urev, {M. V.}",
year = "2019",
month = oct,
day = "1",
doi = "10.1134/S1995423919040049",
language = "English",
volume = "12",
pages = "359--371",
journal = "Numerical Analysis and Applications",
issn = "1995-4239",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "4",

}

RIS

TY - JOUR

T1 - Solving the Pure Neumann Problem by a Finite Element Method

AU - Ivanov, M. I.

AU - Kremer, I. A.

AU - Urev, M. V.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - This paper deals with the solution of the pure Neumann problem for the diffusion equation by a finite element method. First, an extended generalized formulation of the Neumann problem in the Sobolev space H1(Ω) is derived and investigated. Then a discrete analog of this problem is formulated by using standard finite element approximations of the space H1(Ω). An iterative method for solving the corresponding SLAE is proposed. Some examples of solving model problems are used to discuss the numerical properties of the algorithm proposed.

AB - This paper deals with the solution of the pure Neumann problem for the diffusion equation by a finite element method. First, an extended generalized formulation of the Neumann problem in the Sobolev space H1(Ω) is derived and investigated. Then a discrete analog of this problem is formulated by using standard finite element approximations of the space H1(Ω). An iterative method for solving the corresponding SLAE is proposed. Some examples of solving model problems are used to discuss the numerical properties of the algorithm proposed.

KW - consistency conditions

KW - finite elements

KW - orthogonalization of the right-hand side

KW - pure Neumann problem

KW - APPROXIMATION

UR - http://www.scopus.com/inward/record.url?scp=85079571312&partnerID=8YFLogxK

U2 - 10.1134/S1995423919040049

DO - 10.1134/S1995423919040049

M3 - Article

AN - SCOPUS:85079571312

VL - 12

SP - 359

EP - 371

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 4

ER -

ID: 23575045