Geodesic
Discrete-analytic schemes for solving an inverse coefficient heatconduction problem in a layered medium with gradient methods
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 4, pp. 393-408 Cet article a éte moissonné depuis la source Math-Net.Ru

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A method for constructing numerical schemes for inverse coefficient inverse heatconduction problem with boundary measurement data and piecewise-constant coefficients is considered. A set of numerical schemes for a gradient optimization algorithm is presented. The method is based on the combined use of locally-adjoint problems along with approximation methods in the Hilbert spaces. 
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A. V. Penenko. Discrete-analytic schemes for solving an inverse coefficient heatconduction problem in a layered medium with gradient methods. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 4, pp. 393-408. http://geodesic.mathdoc.fr/item/SJVM_2012_15_4_a4/

[1] Penenko V. V., Metody chislennogo modelirovaniya atmosfernykh protsessov, Gidrometizdat, Leningrad, 1981 | MR

[2] Karchevskii A .L., “Korrektnaya skhema deistvii pri chislennom reshenii obratnoi zadachi optimizatsionnym metodom”, Sib. zhurn. vychisl. matematiki (RAN. Sib. otd-nie, Novosibirsk), 11:2 (2008), 139–149

[3] Samarskii A. A., Vabischevich P. N., Vychislitelnaya teploperedacha, LKI, M., 2007

[4] Godunov S. K., Ryabenkii V. S., Raznostnye skhemy: vvedenie v teoriyu, Nauka, M., 1977 | MR

[5] Marchuk G. I., Metody vychislitelnoi matematiki, Lan, M., 2009

[6] Samarskii A. A., Vvedenie v teoriyu raznostnykh skhem, Nauka, M., 1971 | MR | Zbl

[7] Streng G., Fiks D., Teoriya metoda konechnykh elementov, Mir, M., 1984

[8] Infield L., Hull T., “The factorization method”, Reviews of Modern Physics, 23:1 (1951), 21–68 | DOI | MR

[9] El-Mistikawy T. M., Werle M. J., “Numerical method for boundary layers with blowing. The exponential box scheme”, AIAA J., 16 (1978), 749–751 | DOI | Zbl

[10] Berger A. E., Solomon J. M., Ciment M., “An analysis of a uniformly accurate difference method for a singular perturbation problem”, Mathematics of computation, 37:155 (1981), 79–94 | DOI | MR | Zbl

[11] Korneev V. G., “O tochnykh setochnykh skhemakh”, Zhurn. vychisl. matematiki i mat. fiziki, 22:3 (1982), 646–654 | MR | Zbl

[12] Zverev V. G., Goldin V. D., “Raznostnaya skhema dlya resheniya kovektivno-diffuzionnykh zadach teplomassoperenosa”, Vychislitelnye tekhnologii, 7:6 (2002), 24–37 | MR | Zbl

[13] Voevodin A. F., “Metod faktorizatsii dlya lineinykh i kvazilineinykh singulyarno vozmuschennykh kraevykh zadach dlya obyknovennykh differentsialnykh uravnenii”, Sib. zhurn. vychisl. matematiki (RAN. Sib. otd-nie, Novosibirsk), 12:1 (2009), 1–15 | Zbl

[14] Penenko V. V., Tsvetova E. A., “Discrete-analytical methods for the implementation of variational principles in environmental applications”, J. of Computational and Applied Mathematics, 226 (2009), 319–330 | DOI | MR | Zbl

[15] Hasanov A., DuChateau P., Pektas B., “An adjoint problem approach and coarse-fine mesh method for identification of the diffusion coefficient in a linear parabolic equation”, J. of Inverse and Ill-Posed Problems, 14:4 (2006), 1–29 | MR

[16] Penenko V. V., Nekotorye problemy vychislitelnoi i prikladnoi matematiki, ed. M. M. Lavrentev, Nauka, Novosibirsk, 1975, 61–77 | MR

[17] Polak E., Chislennye metody optimizatsii, Mir, M., 1974 | MR | Zbl