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

• Autorzy: Owe Axelsson , János Karátson
• 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.

Słowa kluczowe

EN

Variable coefficients; Harmonic averages; Singular perturbation; Local Green’s functions; Exact difference schemes

Kategorie tematyczne

• 65N80: Fundamental solutions, Green's function methods, etc.
• 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 8
• Strony: 1441-1457

Daty

wydano

2013-08-01

online

2013-05-22

Twórcy

autor

Owe Axelsson

autor

János Karátson

• ELTE University, and MTA-ELTE Numerical Analysis and Large Networks Research Group

Bibliografia

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• [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
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• [11] Matus P., Irkhin V., Lapinska-Chrzczonowicz M., Exact difference schemes for time-dependent problems, Comput. Methods Appl. Math., 2005, 5(4), 422–448
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Identyfikatory

DOI

10.2478/s11533-013-0257-1