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2012 | 10 | 1 | 217-230
Tytuł artykułu

A comparison of some efficient numerical methods for a nonlinear elliptic problem

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to compare and realize three efficient iterative methods, which have mesh independent convergence, and to propose some improvements for them. We look for the numerical solution of a nonlinear model problem using FEM discretization with gradient and Newton type methods. Three numerical methods have been carried out, namely, the gradient, Newton and quasi-Newton methods. We have solved the model problem with these methods, we have investigated the differences between them and analyzed their behavior, efficiency and mesh independence. We also compare the theoretical results to the numerical ones, and finally we propose some improvements which we also investigate.
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
1
Strony
217-230
Opis fizyczny
Daty
wydano
2012-02-01
online
2011-12-09
Twórcy
Bibliografia
  • [1] Brezinski C., A classification of quasi-Newton methods, Numer. Algorithms, 2003, 33(1–4), 123–135 http://dx.doi.org/10.1023/A:1025551602679
  • [2] Dennis J.E., Jr., Moré J.J., Quasi-Newton methods, motivation and theory, SIAM Rev., 1977, 19(1), 46–89 http://dx.doi.org/10.1137/1019005
  • [3] Faragó I., Karátson J., Numerical Solution of Nonlinear Elliptic Problems via Preconditioning Operators: Theory and Applications, Adv. Comput. Theory Pract., 11, Nova Science Publishers, Hauppauge, 2002
  • [4] Karátson J., Faragó I., Variable preconditioning via quasi-Newton methods for nonlinear problems in Hilbert space, SIAM J. Numer. Anal., 2003, 41(4), 1242–1262 http://dx.doi.org/10.1137/S0036142901384277
  • [5] Keller H.B., Elliptic boundary value problems suggested by nonlinear diffusion processes, Arch. Rational Mech. Anal., 1969, 35(5), 363–381 http://dx.doi.org/10.1007/BF00247683
  • [6] Liao S., Su J., Chwang A.T., Series solutions for a nonlinear model of combined convective and radiative cooling of a spherical body, International Journal of Heat and Mass Transfer, 2006, 49(15–16), 2437–2445 http://dx.doi.org/10.1016/j.ijheatmasstransfer.2006.01.030
  • [7] Schlichenmaier R., Bruls J.H.M.J., Schüssler M., Radiative cooling of a hot flux tube in the solar photosphere, Astronomy and Astrophysics, 1999, 349, 961–973
  • [8] Sen M., Analytical Heat Transfer, lecture notes available at http://nd.edu/_msen/Teaching/IntHT/IntHTNotes.pdf
  • [9] Vladimirov V.S., Equations of Mathematical Physics, Mir, Moscow, 1984
  • [10] Zeidler E., Nonlinear Functional Analysis and its Applications. III, Springer, New York, 1985
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0071-6
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