I. A. Kremer, M. V. Urev, “A regularization method for the stationary Maxwell equations in an inhomogeneous conducting medium”, Sib. Zh. Vychisl. Mat., 12:2 (2009), 161–170; Num. Anal. Appl., 2:2 (2009), 131

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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2009, Volume 12, Number 2, Pages 161–170 (Mi sjvm14)

This article is cited in 7 scientific papers (total in 7 papers)

A regularization method for the stationary Maxwell equations in an inhomogeneous conducting medium

I. A. Kremer^a, M. V. Urev^b

^a "Tsentr RITM"
^b Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences

Full-text PDF (211 kB) Citations (7)

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Abstract: This paper considers a problem of defining the vector potential of a magnetic field with a non-standard calibration in an inhomogeneous conducting medium. The problem in question is the one with constraints on the right-hand side and on the solution itself. The generalized and regularized statement of this problem without constraints is proposed and substantiated. This statement of the problem is equivalent to the original generalized problem with constraints.

Key words: stationary Maxwell's equations, vector potential, saddle point problem, regularization, discontinuous coefficients.

Received: 28.10.2008
Revised: 07.11.2008

English version:
Numerical Analysis and Applications, 2009, Volume 2, Issue 2, Pages 131–139
DOI: https://doi.org/10.1134/S1995423909020049

Bibliographic databases:

UDC: 519.632

Language: Russian

Citation: I. A. Kremer, M. V. Urev, “A regularization method for the stationary Maxwell equations in an inhomogeneous conducting medium”, Sib. Zh. Vychisl. Mat., 12:2 (2009), 161–170; Num. Anal. Appl., 2:2 (2009), 131–139

Citation in format AMSBIB

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\pages 161--170

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\transl

\jour Num. Anal. Appl.

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\pages 131--139

\crossref{https://doi.org/10.1134/S1995423909020049}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-67650357961}

Linking options:

https://www.mathnet.ru/eng/sjvm14

https://www.mathnet.ru/eng/sjvm/v12/i2/p161

This publication is cited in the following 7 articles:

M. I. Ivanov, I. A. Kremer, Yu. M. Laevsky, “Solving the Pure Neumann Problem by a Mixed Finite Element Method”, Numer. Analys. Appl., 15:4 (2022), 316
M. I. Ivanov, I. A. Kremer, M. V. Urev, “A solution of the degenerate Neumann problem by the finite element method”, Num. Anal. Appl., 12:4 (2019), 359–371
M. V. Urev, Kh. Kh. Imomnazarov, Jian-Gang Tang, “A boundary value problem for one overdetermined stationary system emerging in the two-velocity hydrodynamics”, Num. Anal. Appl., 10:4 (2017), 347–357
M. I. Ivanov, I. A. Kremer, M. V. Urev, “Regularization method for solving the quasi-stationary Maxwell equations in an inhomogeneous conducting medium”, Comput. Math. Math. Phys., 52:3 (2012), 476–488
M. V. Urev, “Convergence of a discrete scheme in a regularization method for the quasi-stationary Maxwell system in a non-homogeneous conducting medium”, Num. Anal. Appl., 4:3 (2011), 258–269
I. A. Kremer, M. V. Urev, “A Regularization Method for the Quasi-Stationary Maxwell Problem in an Inhomogeneous Conducting Medium”, J. Math. Sci., 188:4 (2013), 378–386
I. A. Kremer, M. V. Urev, “Solution of a regularized problem for a stationary magnetic field in a non-homogeneous conducting medium by a finite element method”, Num. Anal. Appl., 3:1 (2010), 25–38

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Sibirskii Zhurnal Vychislitel'noi Matematiki

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