The wells problem for a~stationary equation of diffusion
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 2, pp. 123-142.

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The paper deals with the wells problem for which non-local boundary conditions are given. It is shown that this problem is equivalent to a mixed formulated problem without wells. For such a statement, an error estimate of the mixed finite element method for the 2D case is studied.
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Yu. M. Laevsky. The wells problem for a~stationary equation of diffusion. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 2, pp. 123-142. http://geodesic.mathdoc.fr/item/SJVM_2010_13_2_a0/

[1] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1966 | MR | Zbl

[2] Chekalin A. N., Chislennye resheniya zadach filtratsii v vodoneftyanykh plastakh, Izd-vo Kazanskogo universiteta, Kazan, 1982

[3] Andreev V. B., Kryakvina S. A., “Setochnye approksimatsii zadachi o skvazhine”, Chislennye metody resheniya zadach filtratsii neszhimaemoi zhidkosti, Izd-vo VTs SO RAN, Novosibirsk, 1975, 51–59

[4] Galanin M. P., Lazareva S. A., Savenkov E. B., Chislennoe issledovanie metoda konechnykh superelementov na primere resheniya zadachi o skvazhine dlya uravneniya Laplasa, Preprint No 79, IPM im. M. V. Keldysha RAN, M., 2005

[5] Konovalov A. N., Problems of Multiphase Fluid Filtration, World Scientific, New Jersey–London–Hong Kong, 1994 | Zbl

[6] Brezzi F., Fortin M., Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991 | MR | Zbl

[7] Grault V., Raviart P-A., Finite Element Methods for Navier–Stokes Equations. Theory and Algorithms, Springer-Verlag, Berlin, 1986 | MR

[8] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1964 | MR

[9] Raviart P-A., Thomas J. M., “A mixed finite element method for 2-nd order elliptic problems”, Mathematical aspects of finite element methods, Lect. Notes in Math., 606, Springer-Verlag, New York, 1977, 292–315 | MR

[10] Ciarlet Ph. G., The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978 | MR | Zbl

[11] Oganesyan L. A., Rukhovets L. A., Variatsionno-raznostnye metody resheniya ellipticheskikh uravnenii, Izd-vo AN ArmSSR, Erevan, 1979

[12] Lyusternik L. A., Sobolev V. I., Elementy funktsionalnogo analiza, Nauka, M., 1965 | MR | Zbl

[13] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1983 | MR