A Mixed Variable Finite Element Method for the Efficient Solution of Nonlinear Diffusion and Potential Flow Equations

  • O. Axelsson
Part of the Notes on Numerical Fluid Mechanics book series (NNFM, volume 11)


A recently developed method ([1]) for the efficient solution of nonlinear partial differential equations of the form \( \frac{\partial }{{\partial x}}\left( {a\frac{{\partial u}}{{1\partial y}}} \right) + \frac{\partial }{{\partial y}}\left( {a\frac{{\partial u}}{{2\partial y}}} \right) + f = o \), where ai = ai(x,y,u,ux,uy,∇u), is further discussed in this paper. The method has applications in many important practical problems.


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  1. [1]
    O. Axelsson and I. Gustafsson, An efficient finite element method for nonlinear diffusion problems, submitted.Google Scholar
  2. [2]
    O. Axelsson and V.A. Barker, Finite Element Solution of Boundary Value Problems. Theory and Computation. Academic Press, Orlando, 1984.Google Scholar
  3. [3]
    O. Axelsson, Numerical Algorithms for indefinite problems, in Elliptic Problem Solvers II, (G. Birkhoff and A. Schoenstadt, eds.), Academic Press, 1984.Google Scholar
  4. [4]
    I. Babuška and J. Osborn, Generalized finite element methods: Their performance and their relation to mixed methods, SIAM J. Numer. Anal. 20 (1983), 510–536.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    P. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland Publ., Amsterdam, 1978.zbMATHGoogle Scholar
  6. [6]
    R.E. Ewing (editor), The Mathematics of Reservoir Simulation, SIAM, Philadelphia, 1984.Google Scholar
  7. [7]
    M.M. Vainberg, Variational method and method of monotone operators in the theory of nonlinear equations, John Wiley, New York, 1973.zbMATHGoogle Scholar

Copyright information

© Springer Fachmedien Wiesbaden 1985

Authors and Affiliations

  • O. Axelsson
    • 1
  1. 1.Department of Mathematics, ToernooiveldUniversity of NijmegenThe Netherlands

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