Solving the Pure Neumann Problem by a Finite Element Method

M. I. Ivanov; I. A. Kremer; M. V. Urev

doi:10.1134/S1995423919040049

Solving the Pure Neumann Problem by a Finite Element Method

M. I. Ivanov, I. A. Kremer, M. V. Urev

Кафедра вычислительной математики ММФ

Результат исследования: Научные публикации в периодических изданиях › статья

Аннотация

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.

Язык оригинала	английский
Страницы (с-по)	359-371
Число страниц	13
Журнал	Numerical Analysis and Applications
Том	12
Номер выпуска	4
DOI	https://doi.org/10.1134/S1995423919040049
Состояние	Опубликовано - 1 окт 2019

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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

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keywords = "consistency conditions, finite elements, orthogonalization of the right-hand side, pure Neumann problem",

author = "Ivanov, {M. I.} and Kremer, {I. A.} and Urev, {M. V.}",

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AU - Kremer, I. A.

AU - Urev, M. V.

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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

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DO - 10.1134/S1995423919040049

M3 - Article

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JO - Numerical Analysis and Applications

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SN - 1995-4239

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Доступ к документу

10.1134/S1995423919040049

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