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 Zh. Vychisl. Mat. Mat. Fiz., 1999, Volume 39, Number 1, Pages 98–123 (Mi zvmmf1756)

On some finite element implementations of iterative methods with splitting of boundary conditions for Stokes and Stokes-type systems in a spherical layer: Axially symmetric case

N. A. Meller, B. V. Pal'tsev, E. G. Khlyupina

Dorodnitsyn Computing Centre of the Russian Academy of Sciences

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English version:
Computational Mathematics and Mathematical Physics, 1999, 39:1, 92–117

Bibliographic databases:
UDC: 519.634
MSC: Primary 76M10; Secondary 76D07

Citation: N. A. Meller, B. V. Pal'tsev, E. G. Khlyupina, “On some finite element implementations of iterative methods with splitting of boundary conditions for Stokes and Stokes-type systems in a spherical layer: Axially symmetric case”, Zh. Vychisl. Mat. Mat. Fiz., 39:1 (1999), 98–123; Comput. Math. Math. Phys., 39:1 (1999), 92–117

Citation in format AMSBIB
\Bibitem{MelPalKhl99} \by N.~A.~Meller, B.~V.~Pal'tsev, E.~G.~Khlyupina \paper On some finite element implementations of iterative methods with splitting of boundary conditions for Stokes and Stokes-type systems in a spherical layer: Axially symmetric case \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 1999 \vol 39 \issue 1 \pages 98--123 \mathnet{http://mi.mathnet.ru/zvmmf1756} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1680462} \zmath{https://zbmath.org/?q=an:1062.76525} \elib{https://elibrary.ru/item.asp?id=13330357} \transl \jour Comput. Math. Math. Phys. \yr 1999 \vol 39 \issue 1 \pages 92--117 

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Erratum

This publication is cited in the following articles:
1. Belash V.O., Pal'tsev B.V., Chechel I.I., “On convergence rate of some iterative methods for bilinear and bicubic finite element schemes for the dissipative Helmholtz equation with large values of a singular parameter”, Russian J Numer Anal Math Modelling, 17:6 (2002), 485–520
2. V. O. Belash, B. V. Pal'tsev, “Bicubic finite-element implementations of methods with splitting of boundary conditions for a Stokes-type system in a strip under the periodicity condition”, Comput. Math. Math. Phys., 42:2 (2002), 188–210
3. B. V. Pal'tsev, I. I. Chechel', “Increasing the rate of convergence of bilinear finite-element realizations of iterative methods by splitting boundary conditions for Stokes-type systems for large values of a singular parameter”, Comput. Math. Math. Phys., 44:11 (2004), 1949–1967
4. Pal'tsev B.V., Chechel I.I., “Finite-element linear second-order accurate (up to the poles) approximations of Laplace–Beltrami, gradient, and divergence operators on a sphere in R-3 in the axisymmetric case”, Doklady Mathematics, 69:2 (2004), 200–207
5. B. V. Pal'tsev, I. I. Chechel', “Second-order accurate (up to the axis of symmetry) finite-element implementations of iterative methods with splitting of boundary conditions for Stokes and stokes-type systems in a spherical layer”, Comput. Math. Math. Phys., 45:5 (2005), 816–857
6. B. V. Pal'tsev, I. I. Chechel', “Second-order accurate method with splitting of boundary conditions for solving the stationary axially symmetric Navier–Stokes problem in spherical gaps”, Comput. Math. Math. Phys., 45:12 (2005), 2148–2165
7. B. V. Pal'tsev, I. I. Chechel', “On the convergence rate and optimization of a numerical method with splitting of boundary conditions for the stokes system in a spherical layer in the axisymmetric case: Modification for thick layers”, Comput. Math. Math. Phys., 46:5 (2006), 820–847
8. M. K. Kerimov, “Boris Vasil'evich Pal'tsev (on the occasion of his seventieth birthday)”, Comput. Math. Math. Phys., 50:7 (2010), 1113–1119
9. B. V. Pal'tsev, M. B. Soloviev, I. I. Chechel', “On the development of iterative methods with boundary condition splitting for solving boundary and initial-boundary value problems for the linearized and nonlinear Navier–Stokes equations”, Comput. Math. Math. Phys., 51:1 (2011), 68–87
10. B. V. Pal'tsev, M. B. Solov'ev, I. I. Chechel', “Numerical study of spherical Couette flows for certain zenith-angle-dependent rotations of boundary spheres at low Reynolds numbers”, Comput. Math. Math. Phys., 56:6 (2012), 940–975
11. B. V. Pal'tsev, M. B. Solov'ev, I. I. Chechel', “On the structure of steady axisymmetric Navier-Stokes flows with a stream function having multiple local extrema in its definite-sign domains”, Comput. Math. Math. Phys., 53:11 (2013), 1696–1719
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