Geodesic
A~scheme of a~finite element method for boundary value problems with non-coordinated degeneration of input data
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 3, pp. 313-324.

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We construct a scheme of a finite element method for boundary value problems with non-coordinated degeneration of input data and singularity of solution. The rate of convergence of an approximate solution of the proposed finite element method to the exact $R_{\nu}$-generalized solution in the weight set $W^1_{2,\nu^*+\beta/2+1}(\Omega,\delta)$ is investigated, the estimation of finite element approximations is established. 
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V. A. Rukavishnikov; E. V. Kuznetsova. A~scheme of a~finite element method for boundary value problems with non-coordinated degeneration of input data. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 3, pp. 313-324. http://geodesic.mathdoc.fr/item/SJVM_2009_12_3_a6/

[1] Rukavishnikov V. A., “O differentsialnykh svoistvakh $R_{\nu}$-obobschennogo resheniya zadachi Dirikhle”, Dokl. AN SSSR, 309:6 (1989), 1318–1320

[2] Rukavishnikov V. A., Rukavishnikova E. I., “Metod konechnykh elementov dlya pervoi kraevoi zadachi s soglasovannym vyrozhdeniem iskhodnykh dannykh”, Dokl. RAN, 338:6 (1994), 731–733 | Zbl

[3] Rukavishnikov V. A., Rukavishnikova H. I., “The finite element method for the third boundary value problem with strong singularity of solution”, ENUMATH 1997. Proc. of Second European Conference on Numerical Mathematics and Advanced Applications, World Scientific Publishing Company, Singapore, 1998, 540–548 | MR | Zbl

[4] Rukavishnikov V. A., Bespalov A. Yu., “Eksponentsialnaya skorost skhodimosti metoda konechnykh elementov dlya zadachi Dirikhle s singulyarnostyu resheniya”, Dokl. RAN, 374,:6 (2000), 727–731 | MR | Zbl

[5] Bespalov A. Yu., Rukavishnikov V. A., “The use singular functions in the h-p version of the finite element method for the Dirichlet problem with degeneration of the input data”, Sib. zhurn. vychisl. matematiki / RAN Sib. otd-nie. — Novosibirsk, 4:4 (2001), 201–228 | MR | Zbl

[6] Rukavishnikov V. A., Rukavishnikova H. I., “A new finite element approach to the boundary value problem with strong singularity of solution”, The First Chinese-Korean Joint Workshop on Recent Advances in Numerical Analysis and Its Applications, Seoul, Korea, 2001, 76–96

[7] Kashuba E. V., Rukavishnikov V. A., “On the $p$-version of the .nite element method for the boundary value problem with singularity”, Sib. zhurn. vychisl. matematiki / RAN Sib. otd-nie. — Novosibirsk, 8:1 (2005), 31–42 | Zbl

[8] Rukavishnikov V. A., “Zadacha Dirikhle s nesoglasovannym vyrozhdeniem iskhodnykh dannykh”, Dokl. RAN, 337:4 (1994), 447–449 | MR | Zbl

[9] Rukavishnikov V. A., “O zadache Dirikhle dlya ellipticheskogo uravneniya vtorogo poryadka s nesoglasovannym vyrozhdeniem iskhodnykh dannykh”, Differents. uravneniya, 32:3 (1996), 402–408 | MR | Zbl

[10] Rukavishnikov V. A., “O edinstvennosti $R_{\nu}$-obobschennogo resheniya dlya kraevykh zadach s nesoglasovannym vyrozhdeniem iskhodnykh dannykh”, Dokl. RAN, 376 (2001), 451–453 | MR | Zbl

[11] Rukavishnikov V. A., Kuznetsova E. V., “Koertsitivnaya otsenka dlya kraevoi zadachi s nesoglasovannym vyrozhdeniem iskhodnykh dannykh”, Differents. uravneniya, 43:4 (2007), 533–543 | MR | Zbl

[12] Rukavishnikov V. A., Kuznetsova E. V., Koertsitivnaya otsenka dlya kraevoi zadachi s nesoglasovannym vyrozhdeniem iskhodnykh dannykh, Preprint Vychislitelnyi tsentr DVO RAN, 85, Khabarovsk, 2005, 28 pp.

[13] Rukavishnikov V. A., Kuznetsova E. V., Skhema metoda konechnykh elementov dlya kraevoi zadachi s nesoglasovannym vyrozhdeniem iskhodnykh dannykh, Preprint Vychislitelnyi tsentr DVO RAN, 108, Khabarovsk, 2007, 15 pp.

[14] S'yarle F. (red.), Metod konechnykh elementov dlya ellipticheskikh zadach, Mir, M., 1980 | MR