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  • Articles  (6)
  • Other Sources
  • AMS(MOS): 65N30  (3)
  • Bifurcation  (3)
  • 1980-1984  (6)
  • Mathematics  (6)
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  • Articles  (6)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 42 (1983), S. 173-194 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider the stationary Navier-Stokes equations, written in terms of the primitive variables, in the case where both the partial differential equations and boundary conditions are inhomogeneous. Under certain conditions on the data, the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed. A conforming finite element method is presented and optimal estimates for the error of the approximate solution are proved. In addition, the convergence properties of iterative methods for the solution of the discrete nonlinear algebraic systems resulting from the finite element algorithm are given. Numerical examples, using an efficient choice of finite element spaces, are also provided.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 44 (1984), S. 371-391 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G 1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The Tricomi problem with Neumann boundary condition is reduced to a degenerate problem in the elliptic region with a non-local boundary condition and to a Cauchy problem in the hyperbolic region. A variational formulation is given to the elliptic problem and a finite element approximation is studied. Also some regularity results in weighted Sobolev spaces are discussed.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 37 (1981), S. 29-48 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A physically based duality theory for first order elliptic systems is shown to be of central importance in connection with the Galerkin finite element solution of these systems. Using this theory in conjunction with a certain hypothesis concerning approximation spaces, optimal error estimates for Galerkin type approximations are demonstrated. An example of a grid which satisfies the hypothesis is given and numerical examples which illustrate the theory are provided.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Acta applicandae mathematicae 2 (1984), S. 101-138 
    ISSN: 1572-9036
    Keywords: 58F ; 70K ; 92 ; Bifurcation ; vector field ; saddle-node singularity ; cusp singularity ; saddle connection ; normal form ; unfolding ; versal family ; population dynamics ; oscillators
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider families of vector fields which exhibit a cusp singularity for some values of the parameters. Algebraic conditions are obtained for these families to have versal properties. This enables the topologically distinct, structurally stable types of phase portrait which occur in the family near to the bifurcation point to be predicted. Applications of these results in population dynamics and oscillation theory are discussed.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 12 (1982), S. 1-11 
    ISSN: 1432-1416
    Keywords: Bifurcation ; Stomata ; Oscillation ; Nonlinear dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Stomata are microscopic openings in leaves of green plants which permit gas exchange. This paper presents a parameter study of a model of a stomatal oscillator first derived by Delwiche and Cooke in 1977. We prove the existence of an unstable limit cycle by using the theory of the Hopf bifurcation. Other bifurcations exhibited by the model are also discussed.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 18 (1983), S. 13-23 
    ISSN: 1432-1416
    Keywords: Ecosystem ; Evolution ; Autonomous oscillations ; issipative structure ; Bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The interrelation between autonomous oscillations in local systems and stable dissipative structures in spatially distributed systems is analyzed. Darwinian evolution in populations comprising the ecosystem is shown to be able to cause the qualitative rearrangements of dynamic modes and smooth appearance of oscillations in local systems. The same evolutionary mechanisms analyzed within bilocal systems, may lead to appearance of dissipative structures (both smooth and sharp).
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