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2013 | 11 | 8 | 1441-1457
Tytuł artykułu

Harmonic averages, exact difference schemes and local Green’s functions in variable coefficient PDE problems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A brief survey is given to show that harmonic averages enter in a natural way in the numerical solution of various variable coefficient problems, such as in elliptic and transport equations, also of singular perturbation types. Local Green’s functions used as test functions in the Petrov-Galerkin finite element method combined with harmonic averages can be very efficient and are related to exact difference schemes.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
8
Strony
1441-1457
Opis fizyczny
Daty
wydano
2013-08-01
online
2013-05-22
Twórcy
  • ELTE University, and MTA-ELTE Numerical Analysis and Large Networks Research Group, karatson@cs.elte.hu
Bibliografia
  • [1] Axelsson O., Stability and error estimates of Galerkin finite element approximations for convection-diffusion equations, IMA J. Numer. Anal., 1981, 1(3), 329–345 http://dx.doi.org/10.1093/imanum/1.3.329
  • [2] Axelsson O., Finite difference methods, In: Encyclopedia of Computational Mechanics, 1, John Wiley & Sons, Chichester, 2004
  • [3] Axelsson O., Glushkov E., Glushkova N., The local Green’s function method in singularly perturbed convection-diffusion problems, Math. Comp., 2009, 78(265), 153–170 http://dx.doi.org/10.1090/S0025-5718-08-02161-3
  • [4] Axelsson O., Gololobov S.V., A combined method of local Green’s functions and central difference method for singularly perturbed convection-diffusion problems, J. Comput. Appl. Math., 2003, 161(2), 245–257 http://dx.doi.org/10.1016/j.cam.2003.08.005
  • [5] Axelsson O., Karátson J., Mesh independent superlinear PCG rates via compact-equivalent operators, SIAM J. Numer. Anal., 2007, 45(4), 1495–1516 http://dx.doi.org/10.1137/06066391X
  • [6] Babuška I., Caloz G., Osborn E., Special finite element methods for a class of second order elliptic problems with rough coefficients, SIAM J. Numer. Anal., 1994, 31(4), 945–981 http://dx.doi.org/10.1137/0731051
  • [7] Efendiev Y., Hou T., Strinopoulos T., Multiscale simulations of porous media flows in flow-based coordinate system, Comput. Geosci., 2008, 12(3), 257–272 http://dx.doi.org/10.1007/s10596-007-9073-7
  • [8] Hemker P.W., A Numerical Study of Stiff Two-Point Boundary Problems, Math. Centre Tracts, 80, Mathematisch Centrum, Amsterdam, 1977
  • [9] Houstis E.N., Rice J.R., High order methods for elliptic partial differential equations with singularities, Internat. J. Numer. Methods Engrg., 1982, 18(5), 737–754 http://dx.doi.org/10.1002/nme.1620180509
  • [10] Lynch R.E., Rice J.R., High accuracy finite difference approximation to solutions of elliptic partial differential equations, Proc. Nat. Acad. Sci. U.S.A., 1978, 75(6), 2541–2544 http://dx.doi.org/10.1073/pnas.75.6.2541
  • [11] Matus P., Irkhin V., Lapinska-Chrzczonowicz M., Exact difference schemes for time-dependent problems, Comput. Methods Appl. Math., 2005, 5(4), 422–448
  • [12] Samarskii A.A., The Theory of Difference Schemes, Monogr. Textbooks Pure Appl. Math., 240, Marcel Dekker, New York, 2001
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0257-1
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