Geodesic
Variational-difference method for estimation of electrical durability of dielectrics
Matematičeskoe modelirovanie, Tome 14 (2002) no. 4, pp. 57-66.

Voir la notice de l'article provenant de la source Math-Net.Ru

The electrostatical boundary-value problem (BVP) for a dielectric in powerful electric field is formulated as the variational problem with taking into account of polarization saturation and current of conductivity. The existence of external charges with no solution of electrostatical BVP is proved. It is treated as beginning of the electric puncture of dielectric. For estimation of puncture conditions the limiting analysis problem (LAP) is formulated. The solution of this original variational problem belongs to the space of scalar functions with bounded variations. As a result, LAP needs a relaxation. The partial relaxation is proposed. It is based on the special discontinuous finite-element approximation. Numerical results show that for solving LAP the proposed technique has the qualitative advantage over the standard continuous finite-element approximation. 
@article{MM_2002_14_4_a4,
     author = {I. A. Brigadnov},
     title = {Variational-difference method for estimation of electrical durability of dielectrics},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {57--66},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2002_14_4_a4/}
}
TY  - JOUR
AU  - I. A. Brigadnov
TI  - Variational-difference method for estimation of electrical durability of dielectrics
JO  - Matematičeskoe modelirovanie
PY  - 2002
SP  - 57
EP  - 66
VL  - 14
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2002_14_4_a4/
LA  - ru
ID  - MM_2002_14_4_a4
ER  - 
%0 Journal Article
%A I. A. Brigadnov
%T Variational-difference method for estimation of electrical durability of dielectrics
%J Matematičeskoe modelirovanie
%D 2002
%P 57-66
%V 14
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2002_14_4_a4/
%G ru
%F MM_2002_14_4_a4
I. A. Brigadnov. Variational-difference method for estimation of electrical durability of dielectrics. Matematičeskoe modelirovanie, Tome 14 (2002) no. 4, pp. 57-66. http://geodesic.mathdoc.fr/item/MM_2002_14_4_a4/

[1] Tamm I. E., Osnovy teorii elektrichestva, Nauka, M., 1989

[2] Kazantsev V. P., Analiticheskaya elektrostatika, Ucheb. posobie. Ch. 1. Variatsionnye printsipy i prostye primery ikh ispolzovaniya, KGU, Krasnoyarsk, 1989

[3] Braun V., Dielektriki, IL, M., 1961

[4] Rez I. S., Poplavko Yu.M., Dielektriki. Osnovnye svoistva i primenenie v elektronike, Radio i svyaz, M., 1989

[5] Dyuvo G., Lions Zh.-L., Neravenstva v mekhanike i fizike, Nauka, M., 1980 | MR

[6] Temam R., Matematicheskie zadachi teorii plastichnosti, Nauka, M., 1991 | MR | Zbl

[7] Brigadnov I. A., “O suschestvovanii predelnoi nagruzki v nekotorykh zadachakh giperuprugosti”, Izv. RAN. MTT, 1993, no. 5, 46–51

[8] Brigadnov I. A., “O matematicheskoi korrektnosti kraevykh zadach elastostatiki dlya giperuprugikh materialov”, Izv. RAN. MTT, 1996, no. 6, 37–46

[9] Brigadnov L. A., “The limited static load in finite elasticity”, Constitutive Models for rubber, A. A. Balkema, Rotterdam, 1999, 37–43

[10] Brigadnov I. A., “Otsenka nesuschei sposobnosti nelineino uprugikh tel”, Izv. RAN. MTT, 2001, no. 1, 6–15

[11] Vorobev A. A, Vorobev G. A., Elektricheskii proboi i razrushenie tverdykh dielektrikov, Vysshaya shkola, M., 1965

[12] Vershinin Yu. N., Elektricheskii proboi tverdykh dielektrikov. Osnovy fenomenologicheskoi teorii i ee tekhnicheskie prilozheniya, Nauka SO, Novosibirsk, 1968

[13] Kufner A., Fuchik S., Nelineinye differentsialnye uravneniya, Nauka, M., 1988 | MR

[14] Dzhusti E., Minimalnye poverkhnosti i funktsii ogranichennoi variatsii, Mir, M., 1989 | MR

[15] Brigadnov I. A., “Discontinuous solutions and their finite element approximation in nonlinear elasticity”, Advanced Computational Methods in Engineering, Shaker Publishing B. V., Maastricht, 1998, 141–148 | MR

[16] Syarle F., Metod konechnykh elementov dlya ellipticheskikh zadach, Mir, M., 1980 | MR

[17] Brigadnov I. A., “O chislennom reshenii kraevykh zadach uprugoplasticheskogo techeniya”, Izv. RAN. MTT, 1992, no. 3, 157–162

[18] Brigadnov I. A., “Chislennoe reshenie kraevoi zadachi giperuprugosti v prirascheniyakh”, Izv. RAN. MTT, 1994, no. 6, 42–50

[19] Brigadnov I. A., “Numerical methods in non-linear elasticity”, Numerical Methods in Engineering, Wiley, Chichester, 1996, 158–163