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Finite Element Method Solution of a Boundary Value Problem for an Elliptic Equation with the Dirac Delta Function on the Right-Hand Side. / Romanov, D. N.; Urev, M. V.

в: Numerical Analysis and Applications, Том 18, № 4, 27.02.2026, стр. 309-319.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Romanov, DN & Urev, MV 2026, 'Finite Element Method Solution of a Boundary Value Problem for an Elliptic Equation with the Dirac Delta Function on the Right-Hand Side', Numerical Analysis and Applications, Том. 18, № 4, стр. 309-319. https://doi.org/10.1134/S1995423925700041

APA

Romanov, D. N., & Urev, M. V. (2026). Finite Element Method Solution of a Boundary Value Problem for an Elliptic Equation with the Dirac Delta Function on the Right-Hand Side. Numerical Analysis and Applications, 18(4), 309-319. https://doi.org/10.1134/S1995423925700041

Vancouver

Romanov DN, Urev MV. Finite Element Method Solution of a Boundary Value Problem for an Elliptic Equation with the Dirac Delta Function on the Right-Hand Side. Numerical Analysis and Applications. 2026 февр. 27;18(4):309-319. doi: 10.1134/S1995423925700041

Author

Romanov, D. N. ; Urev, M. V. / Finite Element Method Solution of a Boundary Value Problem for an Elliptic Equation with the Dirac Delta Function on the Right-Hand Side. в: Numerical Analysis and Applications. 2026 ; Том 18, № 4. стр. 309-319.

BibTeX

@article{f5191d7f36af4c8f8f4e04034b51c2c6,
title = "Finite Element Method Solution of a Boundary Value Problem for an Elliptic Equation with the Dirac Delta Function on the Right-Hand Side",
abstract = "A numerical solution by the finite element method of a homogeneous Dirichlet boundary value problem for an elliptic equation is examined (using a Poisson equation as an example) in a two-dimensional convex polygonal domain with a singular right-hand side given by the Dirac delta function. A theorem on the existence and uniqueness of a generalized solution in the fractional Sobolev space,, is proved. An approach to discrete analysis of the problem using the finite element method is proposed and investigated. The results of numerical experiments for a model problem, obtained using the FreeFem++ software, are presented. They confirm the error estimate of the difference between the discrete and exact solutions derived in the paper.",
keywords = "augmented weak formulation, error estimate, finite element method, fractional Sobolev spaces, singular source term, two-dimensional Poisson equation, двумерное уравнение Пуассона, сингулярный источник, расширенная слабая постановка, дробные пространства Соболева, метод конечных элементов, оценка погрешности",
author = "Romanov, {D. N.} and Urev, {M. V.}",
note = "D. N. Romanov, M. V. Urev. Finite Element Method Solution of a Boundary Value Problem for an Elliptic Equation with the Dirac Delta Function on the Right-Hand Side // Numerical Analysis and Applications. — 2025. — Vol. 18. — no. 4. — P. 309-319. — DOI: 10.1134/S1995423925700041.",
year = "2026",
month = feb,
day = "27",
doi = "10.1134/S1995423925700041",
language = "English",
volume = "18",
pages = "309--319",
journal = "Numerical Analysis and Applications",
issn = "1995-4239",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "4",

}

RIS

TY - JOUR

T1 - Finite Element Method Solution of a Boundary Value Problem for an Elliptic Equation with the Dirac Delta Function on the Right-Hand Side

AU - Romanov, D. N.

AU - Urev, M. V.

N1 - D. N. Romanov, M. V. Urev. Finite Element Method Solution of a Boundary Value Problem for an Elliptic Equation with the Dirac Delta Function on the Right-Hand Side // Numerical Analysis and Applications. — 2025. — Vol. 18. — no. 4. — P. 309-319. — DOI: 10.1134/S1995423925700041.

PY - 2026/2/27

Y1 - 2026/2/27

N2 - A numerical solution by the finite element method of a homogeneous Dirichlet boundary value problem for an elliptic equation is examined (using a Poisson equation as an example) in a two-dimensional convex polygonal domain with a singular right-hand side given by the Dirac delta function. A theorem on the existence and uniqueness of a generalized solution in the fractional Sobolev space,, is proved. An approach to discrete analysis of the problem using the finite element method is proposed and investigated. The results of numerical experiments for a model problem, obtained using the FreeFem++ software, are presented. They confirm the error estimate of the difference between the discrete and exact solutions derived in the paper.

AB - A numerical solution by the finite element method of a homogeneous Dirichlet boundary value problem for an elliptic equation is examined (using a Poisson equation as an example) in a two-dimensional convex polygonal domain with a singular right-hand side given by the Dirac delta function. A theorem on the existence and uniqueness of a generalized solution in the fractional Sobolev space,, is proved. An approach to discrete analysis of the problem using the finite element method is proposed and investigated. The results of numerical experiments for a model problem, obtained using the FreeFem++ software, are presented. They confirm the error estimate of the difference between the discrete and exact solutions derived in the paper.

KW - augmented weak formulation

KW - error estimate

KW - finite element method

KW - fractional Sobolev spaces

KW - singular source term

KW - two-dimensional Poisson equation

KW - двумерное уравнение Пуассона

KW - сингулярный источник

KW - расширенная слабая постановка

KW - дробные пространства Соболева

KW - метод конечных элементов

KW - оценка погрешности

UR - https://www.mendeley.com/catalogue/a2832d8d-2383-32bc-b51c-6cee06b214d0/

UR - https://www.scopus.com/pages/publications/105031599121

U2 - 10.1134/S1995423925700041

DO - 10.1134/S1995423925700041

M3 - Article

VL - 18

SP - 309

EP - 319

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 4

ER -

ID: 75591960