RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb., 1997, Volume 188, Number 3, Pages 143–160 (Mi msb214)  

This article is cited in 30 scientific papers (total in 30 papers)

Estimates of the rate of convergence of projective and projective-difference methods for weakly solvable parabolic equations

V. V. Smagin

Voronezh State University

Abstract: We consider a weakly solvable parabolic problem in a separable Hilbert space. We seek approximations to the exact solution by projective and projective-difference methods. In this connection the discretization of the problem with respect to the spatial variables is carried out by the semidiscrete method of Galerkin, and with respect to time by the implicit method of Euler. In this paper we establish a coercive mean-square error estimate for the approximate solutions. We illustrate the effectiveness of these estimates with parabolic equations of second order with Dirichlet or Neumann boundary conditions in projective subspaces of finite element type.

DOI: https://doi.org/10.4213/sm214

Full text: PDF file (266 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 1997, 188:3, 465–481

Bibliographic databases:

UDC: 517.9
MSC: Primary 35K20; Secondary 65M15, 65M60
Received: 04.03.1996

Citation: V. V. Smagin, “Estimates of the rate of convergence of projective and projective-difference methods for weakly solvable parabolic equations”, Mat. Sb., 188:3 (1997), 143–160; Sb. Math., 188:3 (1997), 465–481

Citation in format AMSBIB
\Bibitem{Sma97}
\by V.~V.~Smagin
\paper Estimates of the~rate of convergence of projective and projective-difference methods for weakly solvable parabolic equations
\jour Mat. Sb.
\yr 1997
\vol 188
\issue 3
\pages 143--160
\mathnet{http://mi.mathnet.ru/msb214}
\crossref{https://doi.org/10.4213/sm214}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1462027}
\zmath{https://zbmath.org/?q=an:0887.35068}
\transl
\jour Sb. Math.
\yr 1997
\vol 188
\issue 3
\pages 465--481
\crossref{https://doi.org/10.1070/sm1997v188n03ABEH000214}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1997XP47500007}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0031286031}


Linking options:
  • http://mi.mathnet.ru/eng/msb214
  • https://doi.org/10.4213/sm214
  • http://mi.mathnet.ru/eng/msb/v188/i3/p143

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. E. Zhelezovsky, N. N. Bukesova, “Error estimates for the projection method for an abstract quasilinear hyperbolic equation”, Russian Math. (Iz. VUZ), 43:5 (1999), 90–92  mathnet  mathscinet  zmath  elib
    2. N. N. Bukesova, S. E. Zhelezovsky, “Convergence rate of the Galerkin method for a class of quasilinear operator differential equations”, Comput. Math. Math. Phys., 39:9 (1999), 1455–1467  mathnet  mathscinet  zmath  elib
    3. V. V. Smagin, “Mean-square estimates for the error of a projection-difference method for parabolic equations”, Comput. Math. Math. Phys., 40:6 (2000), 868–879  mathnet  mathscinet  zmath  elib
    4. S. E. Zhelezovsky, “Estimates for the Rate of Convergence of the Galerkin Method for Abstract Hyperbolic Equations”, Math. Notes, 69:2 (2001), 196–206  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Zhelezovskii, SE, “Error estimates of the Galerkin method for quasilinear hyperbolic equations”, Differential Equations, 37:7 (2001), 988  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    6. Siberian Math. J., 42:3 (2001), 568–578  mathnet  crossref  mathscinet  zmath  isi  scopus
    7. Smagin, VV, “Projection-difference methods for the approximate solution of parabolic equations with nonsymmetric operators”, Differential Equations, 37:1 (2001), 128  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    8. Lyashko, AD, “Investigation of the projection method for degenerate nonstationary equations”, Differential Equations, 38:7 (2002), 1050  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    9. V. V. Smagin, “Strong-Norm Error Estimates for the Projective-Difference Method for Parabolic Equations with Modified Crank–Nicolson Scheme”, Math. Notes, 74:6 (2003), 864–873  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. Lyashko, AD, “Semidiscrete finite element schemes for nonstationary degenerating equations”, Differential Equations, 39:7 (2003), 1007  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    11. V. V. Smagin, “On the Rate of Convergence of Projection-Difference Methods for Smoothly Solvable Parabolic Equations”, Math. Notes, 78:6 (2005), 841–852  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. Lyashko, AD, “Error estimates for projection-difference schemes for degenerate nonstationary equations”, Differential Equations, 42:7 (2006), 1013  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    13. Vinogradova, PV, “Error estimates for a projection-difference method for a linear differential-operator equation”, Differential Equations, 44:7 (2008), 970  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    14. P. V. Vinogradova, A. G. Zarubin, “Error estimates for the Galerkin method as applied to time-dependent equations”, Comput. Math. Math. Phys., 49:9 (2009), 1567–1575  mathnet  crossref  zmath  isi  elib  elib
    15. Vinogradova, P, “Convergence estimates of a projection-difference method for an operator-differential equation”, Journal of Computational and Applied Mathematics, 231:1 (2009), 1  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    16. Vinogradova, P, “Projection Method for Cauchy Problem for an Operator-Differential Equation”, Numerical Functional Analysis and Optimization, 30:1–2 (2009), 148  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    17. Smagin V.V., “Slabaya razreshimost zadachi Koshi dlya parabolicheskogo uravneniya i srednekvadratichnaya skhodimost poludiskretnogo metoda Galerkina”, Vestn. Voronezhskogo gos. un-ta. Ser.: Fiz. Matem., 2009, no. 1, 164–169  elib
    18. Sotnikov D.S., “Skhodimost proektsionno-raznostnogo metoda dlya kvazileneinykh parabolicheskikh zadach v usloviyakh obobschennoi razreshimosti”, Vestn. Voronezhskogo gos. un-ta. Ser.: Fiz. Matem., 2009, no. 1, 170–176  elib
    19. Smagin V.V., “O skorosti skhodimosti metoda Galerkina dlya nelineinogo parabolicheskogo uravneniya”, Vestn. Voronezhskogo gos. un-ta. Ser.: Fiz. Matem., 2009, no. 2, 121–125  elib
    20. Sotnikov D.S., “Skhodimost v silnykh normakh proektsionno-raznostnogo metoda dlya kvazilineinogo parabolicheskogo uravneniya”, Vestn. Voronezhskogo gos. un-ta. Ser.: Fiz. Matem., 2009, no. 2, 126–133  elib
    21. P. V. Vinogradova, “Error estimates for projection-difference methods for differential equations with differentiable operators”, Russian Math. (Iz. VUZ), 54:7 (2010), 1–11  mathnet  crossref  mathscinet  elib
    22. Smagin V.V., Sotnikov D.S., “Mean-square accuracy estimates of a projection-difference method for weakly solvable quasilinear parabolic equations”, Differential Equations, 46:4 (2010), 598–606  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    23. Vinogradova P., “Convergence Rate of Galerkin Method for a Certain Class of Nonlinear Operator-Differential Equations”, Numerical Functional Analysis and Optimization, 31:3 (2010), 339–365  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    24. A. V. Razgulin, “A weighted estimate for the rate of convergence of a projection-difference scheme for a parabolic equation and its application to the approximation of the initial-data control problem”, Comput. Math. Math. Phys., 50:6 (2010), 969–983  mathnet  crossref  mathscinet  adsnasa  isi  elib  elib
    25. V. A. Grebennikov, A. V. Razgulin, “Weighted estimate for the convergence rate of a projection difference scheme for a quasilinear parabolic equation”, Comput. Math. Math. Phys., 51:7 (2011), 1208–1221  mathnet  crossref  mathscinet  isi  elib
    26. Tyong Kh.N., “Skhodimost proektsionno-raznostnogo metoda priblizhennogo resheniya parabolicheskogo uravneniya s integralnym usloviem na reshenie”, Vestnik voronezhskogo gosudarstvennogo universiteta. seriya: fizika. matematika, 2011, no. 1, 202–208  elib
    27. Smagin V.V., “O skhodimosti metoda galerkina dlya gladko razreshimogo nelineinogo parabolicheskogo uravneniya”, Vestnik voronezhskogo gosudarstvennogo universiteta. seriya: fizika. matematika, 2012, no. 1, 195–195  zmath  elib
    28. Smagin V.V., “Projection-Difference Method With the Crank-Nicolson Scheme in Time For the Approximate Solution of a Parabolic Equation With An Integral Condition For the Solution”, Differ. Equ., 51:1 (2015), 116–126  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    29. A. A. Petrova, V. V. Smagin, “Convergence of the Galyorkin method of approximate solving of parabolic equation with weight integral condition on a solution”, Russian Math. (Iz. VUZ), 60:8 (2016), 42–51  mathnet  crossref  isi
    30. Petrova A.A., “Convergence of a Projection-Difference Method For the Approximate Solution of a Parabolic Equation With a Weighted Integral Condition on the Solution”, Differ. Equ., 54:7 (2018), 957–970  crossref  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:290
    Full text:72
    References:28
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019