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On the numerical solution of nonlinear partial differential equations on divergence form

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References

  1. M.M. Vainberg, Variational method and method of monotone operators in the theory of nonlinear equations, Wiley, 1973.

    Google Scholar 

  2. O. Axelsson, U. Nävert, On a graphical package for nonlinear partial differential equation problems, Proc. IFIP Congress 77, B. Gilchrist (ed.), North-Holland Publ. Comp. (1977).

    Google Scholar 

  3. O. Axelsson, A class of iterative methods for finite element equations, Comp. Meth. Appl. Mech. Engrg 9(1976), 123–137.

    Article  MathSciNet  MATH  Google Scholar 

  4. O. Axelsson, T. Steihaug, Some computational aspects in the numerical solution of parabolic equations, in preparation.

    Google Scholar 

  5. R. Bartels, J.W. Daniel, A conjugate gradient approach to nonlinear elliptic boundary value problems in irregular regions, CNA63, Center for Numerical Analysis, Austin, Texas, 1973.

    MATH  Google Scholar 

  6. P. Concus, G.H. Golub, D. O'Leary, Numerical solution of nonlinear elliptic partial differential equations, STAN-CS-76-585, Computer Science Departmetn, Stanford University, 1976.

    Google Scholar 

  7. D. O'Leary, Hybrid conjugate gradient algorithms, STAN-CS-76-548, Computer Science Department, Stanford University, 1976.

    Google Scholar 

  8. O. Axelsson, Error estimates for Galerkin methods for quasilinear parabolic and elliptic differential equations in divergence form, Numer. Math. 28, 1–14, (1977).

    Article  MathSciNet  MATH  Google Scholar 

  9. T. Dupont, Some L2error estimates for parabolic Galerkin method in The mathematical foundations of the finite element method with applications to partial differential equations (A.K. Aziz, ed.) 491–504. Academic Press N.Y. 1972.

    Google Scholar 

  10. I. Hlavàcek, On a semi-variational method for parabolic equations I, Aplikaee Matematiky 17(1972), 327–351.

    MathSciNet  MATH  Google Scholar 

  11. J. Douglas, T. Dupont, A Galerkin method for a nonlinear Dirichlet problem, Math. Comp. 29(1975), 689–696.

    Article  MathSciNet  MATH  Google Scholar 

  12. M.F. Wheeler, A priori L2error estimates for Galerkin approximations to parabolic partial differential equations, SIAM J. Numer. Anal. 10(1973), 713–759.

    Google Scholar 

  13. J.E. Dendy, Galerkin's meghod for some highly nonlinear problems, SIAM J. Numer. Anal. 14(1977), 327–347.

    Article  MathSciNet  MATH  Google Scholar 

  14. H.D. Mittelmann, Numerische Behandlung nichtlinearer Randwertproblemen mit finiten Elementen, Computing 18, 67–77 (1977).

    Article  MathSciNet  MATH  Google Scholar 

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Jiří Fábera

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© 1979 Spring-Verlag

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Axelsson, O. (1979). On the numerical solution of nonlinear partial differential equations on divergence form. In: Fábera, J. (eds) Equadiff IV. Lecture Notes in Mathematics, vol 703. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067250

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  • DOI: https://doi.org/10.1007/BFb0067250

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09116-5

  • Online ISBN: 978-3-540-35519-9

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