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Zh. Vychisl. Mat. Mat. Fiz., 1966, Volume 6, Number 5, Pages 861–883 (Mi zvmmf7409)  

This article is cited in 25 scientific papers (total in 26 papers)

On the convergence of a relaxation method with natural constraints on the elliptic operator

N. S. Bakhvalov

Moscow

Full text: PDF file (2218 kB)

English version:
USSR Computational Mathematics and Mathematical Physics, 1966, 6:5, 101–135

Bibliographic databases:

UDC: 518:517.944/.947
MSC: 65-XX
Received: 27.11.1965

Citation: N. S. Bakhvalov, “On the convergence of a relaxation method with natural constraints on the elliptic operator”, Zh. Vychisl. Mat. Mat. Fiz., 6:5 (1966), 861–883; U.S.S.R. Comput. Math. Math. Phys., 6:5 (1966), 101–135

Citation in format AMSBIB
\Bibitem{Bak66}
\by N.~S.~Bakhvalov
\paper On the convergence of a relaxation method with natural constraints on the elliptic operator
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1966
\vol 6
\issue 5
\pages 861--883
\mathnet{http://mi.mathnet.ru/zvmmf7409}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=0215538}
\zmath{https://zbmath.org/?q=an:0154.41002}
\transl
\jour U.S.S.R. Comput. Math. Math. Phys.
\yr 1966
\vol 6
\issue 5
\pages 101--135
\crossref{https://doi.org/10.1016/0041-5553(66)90118-2}


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    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. R. P. Fedorenko, “Iterative methods for elliptic difference equations”, Russian Math. Surveys, 28:2 (1973), 129–195  mathnet  crossref  mathscinet  zmath
    2. G. K. Berikelashvili, “The convergence in $W_2^2$ of a difference solution of the Dirichlet problem”, U.S.S.R. Comput. Math. Math. Phys., 30:2 (1990), 89–92  mathnet  crossref  mathscinet  zmath
    3. V. G. Belsky, “A multigrid method for solving variational inequalities”, U.S.S.R. Comput. Math. Math. Phys., 31:9 (1991), 1–8  mathnet  mathscinet  zmath  isi
    4. I. E. Koshelev, “Numerical solution of the linear Fredholm equation of the first kind by the multigrid method”, Russian Math. (Iz. VUZ), 42:2 (1998), 31–36  mathnet  mathscinet  zmath
    5. N. S. Bakhvalov, “Efficient methods for stiff multidimensional multiparametric problems”, Comput. Math. Math. Phys., 39:12 (1999), 1938–1966  mathnet  mathscinet  zmath  elib
    6. V. G. Korneev, Ya. Fish, “Two-level methods, based on aggregation, for solving three-dimensional problems”, Russian Math. (Iz. VUZ), 44:11 (2000), 39–57  mathnet  mathscinet  zmath
    7. Yu. K. Dem'yanovich, “On the embedding of minimal spline spaces”, Comput. Math. Math. Phys., 40:7 (2000), 970–986  mathnet  mathscinet  zmath
    8. M. A. Ol'shanskii, “An analysis of the multigtrid method for the convection-diffusion equations with the Dirichlet boundary conditions”, Comput. Math. Math. Phys., 44:8 (2004), 1374–1403  mathnet  mathscinet  zmath
    9. M. K. Kerimov, “Academician Nikolai Sergeevich Bakhvalov (on the occasion of his seventieth birthday)”, Comput. Math. Math. Phys., 45:4 (2005), 539–549  mathnet  mathscinet  zmath  elib
    10. Yu. K. Dem'yanovich, “Embedded Spaces of Trigonometric Splines and Their Wavelet Expansion”, Math. Notes, 78:5 (2005), 615–630  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. L. A. Krukier, G. V. Muratova, “Reshenie statsionarnoi zadachi konvektsii-diffuzii s preobladayuschei konvektsiei mnogosetochnym metodom so spetsialnymi sglazhivatelyami”, Matem. modelirovanie, 18:5 (2006), 63–72  mathnet  mathscinet  zmath
    12. Yu. S. Vasilev, V. G. Korneev, “Tretii komponent poznaniya — nauchnye kompyuternye supervychisleniya”, Uchen. zap. Kazan. gos. un-ta. Ser. Fiz.-matem. nauki, 149, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2007, 6–32  mathnet
    13. S. I. Martynenko, “Formalizatsiya vychislenii pri chislennom reshenii kraevykh zadach”, Uchen. zap. Kazan. gos. un-ta. Ser. Fiz.-matem. nauki, 150, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2008, 76–90  mathnet  zmath
    14. S. I. Martynenko, “Robust multigrid technique”, Math. Models Comput. Simul., 2:2 (2010), 232–244  mathnet  crossref  mathscinet  zmath
    15. M. E. Ladonkina, O. Yu. Milyukova, V. F. Tishkin, “A numerical method for solving diffusion-type equations based on a multigrid method”, Comput. Math. Math. Phys., 50:8 (2010), 1367–1390  mathnet  crossref  mathscinet  adsnasa  isi
    16. K. N. Volkov, “Multigrid techniques as applied to gasdynamic simulation on unstructured meshes”, Comput. Math. Math. Phys., 50:11 (2010), 1837–1850  mathnet  crossref  adsnasa  isi
    17. A. I. Zadorin, N. A. Zadorin, “Interpolyatsiya funktsii s pogransloinymi sostavlyayuschimi i ee primenenie v dvukhsetochnom metode”, Sib. elektron. matem. izv., 8 (2011), 247–267  mathnet
    18. Milyukova O.Yu., Tishkin V.F., “Chislennyi metod resheniya uravneniya teploprovodnosti na treugolnykh setkakh na osnove mnogosetochnogo metoda”, Preprinty IPM im. M.V. Keldysha, 2011, no. 29, 1–16  elib
    19. O. Yu. Milyukova, V. F. Tishkin, “Chislennyi metod resheniya uravneniya teploprovodnosti na treugolnykh setkakh na osnove mnogosetochnogo metoda”, Preprinty IPM im. M. V. Keldysha, 2011, 029, 16 pp.  mathnet
    20. O. Yu. Milyukova, V. F. Tishkin, “Chislennyi metod resheniya uravneniya teploprovodnosti s razryvnym koeffitsientom na osnove mnogosetochnogo metoda”, Preprinty IPM im. M. V. Keldysha, 2013, 064, 19 pp.  mathnet
    21. Muratova G., Andreeva E., “Multigrid Method For Fluid Dynamic Problems”, J. Comput. Math., 32:3 (2014), 233–247  crossref  mathscinet  zmath  isi  elib
    22. O. Yu. Milyukova, V. F. Tishkin, “A multigrid method for the heat equation with discontinuous coefficients with the special choice of grids”, Math. Models Comput. Simul., 8:2 (2016), 118–128  mathnet  crossref  mathscinet  elib
    23. S. I. Martynenko, V. M. Volokhov, L. S. Yanovskiy, “Parallel multigrid technique: reduction to independent problems”, Math. Models Comput. Simul., 9:1 (2017), 120–126  mathnet  crossref  elib
    24. A. B. Sviridenko, “Pryamye multiplikativnye metody dlya razrezhennykh matrits. Nesimmetrichnye lineinye sistemy”, Kompyuternye issledovaniya i modelirovanie, 8:6 (2016), 833–860  mathnet  crossref
    25. K. N. Volkov, A. S. Kozelkov, S. V. Lashkin, N. V. Tarasova, A. V. Yalozo, “A parallel implementation of the algebraic multigrid method for solving problems in dynamics of viscous incompressible fluid”, Comput. Math. Math. Phys., 57:12 (2017), 2030–2046  mathnet  crossref  crossref  isi  elib
    26. Feng W., Guo Zh., Lowengrub J.S., Wise S.M., “A Mass-Conservative Adaptive Fas Multigrid Solver For Cell-Centered Finite Difference Methods on Block-Structured, Locally-Cartesian Grids”, J. Comput. Phys., 352 (2018), 463–497  crossref  isi
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