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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2009, Volume 49, Number 9, Pages 1643–1651 (Mi zvmmf4756)  
This article is cited in 12 scientific papers (total in 12 papers)

Error estimates for the Galerkin method as applied to time-dependent equations

P. V. Vinogradova, A. G. Zarubin

Far Eastern State Transport University, ul. Serysheva 47, Khabarovsk, 680021, Russia
Full-text PDF (948 kB) Citations (12)
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Abstract: A projection method is studied as applied to the Cauchy problem for an operator-differential equation with a non-self-adjoint operator. The operator is assumed to be sufficiently smooth. The linear spans of eigenelements of a self-adjoint operator are used as projection subspaces. New asymptotic estimates for the convergence rate of approximate solutions and their derivatives are obtained. The method is applied to initial-boundary value problems for parabolic equations.
Key words: Galerkin method, operator equation, Hilbert space, Cauchy problem, convergence rate, orthoprojector, parabolic equations.
Received: 06.10.2008
Revised: 12.01.2009
English version:
Computational Mathematics and Mathematical Physics, 2009, Volume 49, Issue 9, Pages 1567–1575
DOI: https://doi.org/10.1134/S0965542509090115
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: P. V. Vinogradova, A. G. Zarubin, “Error estimates for the Galerkin method as applied to time-dependent equations”, Zh. Vychisl. Mat. Mat. Fiz., 49:9 (2009), 1643–1651; Comput. Math. Math. Phys., 49:9 (2009), 1567–1575
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/zvmmf/v49/i9/p1643
    • This publication is cited in the following 12 articles:
    1. Elena S. Efimova, Irina M. Tikhonova, AIP Conference Proceedings, 2048, 2018, 040002  crossref
    2. E. S. Efimova, “Statsionarnyi metod Galerkina dlya polulineinogo neklassicheskogo uravneniya vysokogo poryadka s menyayuschimsya napravleniem vremeni”, Matematicheskie zametki SVFU, 24:1 (2017), 16–25  mathnet  elib
    3. I. E. Egorov, E. S. Efimova, “Kraevaya zadacha dlya uravneniya tretego poryadka, ne razreshennogo otnositelno starshei proizvodnoi”, Matematicheskie zametki SVFU, 24:4 (2017), 28–36  mathnet  crossref  elib
    4. P. V. Vinogradova, A. M. Samusenko, I. S. Manzhula, “Asymptotic estimate of a Petrov–Galerkin method for nonlinear operator-differential equation”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:4 (2016), 17–29  mathnet  crossref  elib
    5. I. M. Tikhonova, “Primenenie statsionarnogo metoda Galerkina k pervoi kraevoi zadache dlya uravneniya smeshannogo tipa vysokogo poryadka”, Matematicheskie zametki SVFU, 23:4 (2016), 73–81  mathnet  elib
    6. V. E. Fedorov, I. M. Tikhonova, “O statsionarnom metode Galerkina v odnoi kraevoi zadache dlya uravneniya smeshannogo tipa vtorogo poryadka”, Matematicheskie zametki SVFU, 23:4 (2016), 82–90  mathnet  elib
    7. I. E. Egorov, I. M. Tikhonova, “Modifitsirovannyi metod Galerkina dlya zadachi Vragova”, Sib. elektron. matem. izv., 12 (2015), 732–742  mathnet  crossref
    8. P. V. Vinogradova, T. E. Koroleva, “One projection method for linear equation of third order”, Russian Math. (Iz. VUZ), 58:11 (2014), 22–27  mathnet  crossref
    9. E. S. Efimova, I. E. Egorov, M. S. Kolesova, “Error Estimation for Stationary Galerkin Method for Semilinear Parabolic Equation with Changing Direction of Time”, J. Math. Sci., 213:6 (2016), 838–843  mathnet  mathnet  crossref
    10. Egorov I.E., Tikhonova I.M., “O skorosti skhodimosti statsionarnogo metoda galerkina dlya uravneniya smeshannogo tipa”, Vestn. Yuzhno-Uralskogo gosyu un-ta. Ser. Matematicheskoe modelirovanie i programmirovanie, 2012, no. 40, 53–58  zmath  elib
    11. Egorov I.E., Efimova E.S., “Otsenka pogreshnosti statsionarnogo metoda Galërkina dlya vyrozhdayuschegosya parabolicheskogo uravneniya”, Matematicheskie zametki YaGU, 19:1 (2012), 27–33  mathscinet  zmath  elib
    12. I. E. Egorov, I. M. Tikhonova, “O skorosti skhodimosti statsionarnogo metoda Galerkina dlya uravneniya smeshannogo tipa”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 14, 53–58  mathnet
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