Iterative algorithms for higher order finite element schemes
Matematičeskoe modelirovanie, Tome 16 (2004) no. 7, pp. 117-128.

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An iterative method for the solution of partial differential equation by higher order finite element method (FEM) on unstructured grids is presented. The algorithms corresponding to lagrangean and hierarchical FEM bases are designed and studied. The results of numerical experiments for a set of the problems (diffusion, convection-diffusion, Euler, Navier–Stokes) are given to show capability of the algorithms.
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V. T. Zhukov; O. B. Feodoritova; D. P. Young. Iterative algorithms for higher order finite element schemes. Matematičeskoe modelirovanie, Tome 16 (2004) no. 7, pp. 117-128. http://geodesic.mathdoc.fr/item/MM_2004_16_7_a11/

[1] V. T. Zhukov, O. B. Feodoritova, Iteratsionnyi metod dlya konechno-elementnykh skhem vysokogo poryadka. Chast I, Preprint IPM im. M. V. Keldysha No 7, 2003

[2] V. T. Zhukov, O. B. Feodoritova, N. D. Novikova, Iteratsionnyi metod dlya konechno-elementnykh skhem vysokogo poryadka. Chast II, Preprint IPM im. M. V. Keldysha No 43, 2003

[3] O. Axelsson, “Improving additive and multiplicative preconditioners for two-level matrices by congruence transformations”, Proceedings of the Int. Conference on Computational Mathematics, Novosibirsk, 2002, 3–16 | MR

[4] V. Korneev, Dzh. Flaerti, T. Oden, Dzh. Fish, “Additivnye algoritmy Shvartsa dlya diskretizatsii na treugolnykh setkakh”, Matematicheskoe modelirovanie, 14:2 (2002), 61–94 | MR | Zbl

[5] V. Venkatakrishnan, S. Allmaras, D. Kamenetskii, F. Johnson, Higher Order Schemes for the Compressible Navier-Stokes Equations, AIAA-2003-3987, 2003 | Zbl

[6] A. A. Martynov, S. Yu. Medvedev, “Nadezhnyi sposob postroeniya setok s vytyanutymi yacheikami”, Postroenie raschetnykh setok: teoriya i prilozheniya, eds. S. A. Ivanenko, V. A. Garanzh, VTs RAN, Moskva, 2002, 266–275

[7] V. T. Zhukov, N. D. Novikova, L. G. Strakhovskaya, R. P. Fedorenko, O. B. Feodoritova, “Primenenie metoda konechnykh superelementov dlya resheniya zadach konvektsii-diffuzii”, Matematicheskoe modelirovanie, 14:11 (2002), 78–92 | MR | Zbl

[8] T. J. R. Hughes, “Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier–Stokes equations”, Int. Journ. for Numer. Met. in Fluids, 7 (1987), 1261–1275 | DOI | MR | Zbl

[9] Y. Saad and M. H. Schultz, “GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems”, SIAM J. Scient. Statist. Comput., 7:30 (1986), 856–869 | DOI | MR | Zbl

[10] G. Karypis and V. Kumar, “Multilevel k-way partitioning scheme for irregular graphs”, J. of Parallel and Distributed Computing, 48:1 (1998), 96–129 | DOI | MR

[11] L. F. Pavarino, O. B. Widlund, “A polylogarithmic bound for an iterative substructuring method for spectral elements in three dimension”, SIAM J. Numer. Anal., 33 (1996), 1303–1335 | DOI | MR | Zbl

[12] L. F. Pavarino, O. B. Widlund, “Iterative substructuring methods for spectral elements: problems in three dimensions based on numerical quadrature. Approximation theory and applications”, Comput. Math. Appl., 33:1–2 (1997), 193–209 | DOI | MR | Zbl

[13] W. Cao, B. Guo, “A preconditioner with inexact element face solvers for three dimensional p-version finite element methods”, J. Comput. Appl. Math., 144 (2002), 131–144 | DOI | MR | Zbl

[14] L. D. Landau, M. L. Lifshits, Mekhanika sploshnykh sred, Tekh.-Teor. Izdat., M., 1954

[15] K. Gerdes, J. M. Melenk, D. Schotzau and C. Schwab, “The $hp$-Version of the Streamline Diffusion Finite Element Method in Two Space Dimensions”, Math. Models and Methods in Applied Sciences, 11:2 (2001), 301–337 | DOI | MR | Zbl