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  • Articles  (91)
  • Other Sources
  • Engineering  (85)
  • AMS(MOS): 65N30  (3)
  • Bifurcation  (3)
  • 1980-1984  (91)
  • Mathematics  (91)
  • 1
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1505-1520 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper deals with the theoretical and numerical treatment of dynamic unilateral problems. The governing equations are formulated as an equivalent variational inequality expressing D' Alembert's principle in its inequality form. The discretization with respect to time and space leads to a static nonlinear programming problem which is solved by an appropriate algorithm. Some properties of dynamic unilateral problems are outlined and the influence of several parameters on the solution is investigated by means of numerical examples.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1067-1084 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A linear model for the solidification of a dilute binary alloy is presented. In this model the solidus and liquidus curves are linear. As a consequence internal energy depends linearly upon temperature and concentration. The formulation is a generalization of the well-known enthalpy method to treat a phase change problem involving coupled heat and mass transfer. Both analytic and numerical formulations are given. Results from the latter are presented and compared with an explicit solution of Rubinstein for a Stefan-like problem posed in a semi-infinite slab. Some remarks on the behaviour of the explicit solution are given.
    Additional Material: 5 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1169-1174 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 2 Tab.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 573-599 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dynamic stress field and its concentrations around holes of arbitrary shape in infinitely extended bodies under plane stress or plane strain conditions are numerically determined. The material may be linear elastic or viscoelastic, while the dynamic load consists of plane compressional waves of harmonic or general transient nature. The method consists of applying the Laplace transform with respect to time to the governing equations of motion and formulating and solving the problem numerically in the transfomed domain by the boundary integral equation method. The stress field can then be obtaind by a numerical inversion of the trasformed solution. The correspondence principle is invoked for the case of viscoelastic material behavious. The method is simplified for the case of harmonic waves where no numerical inversion is involved.
    Additional Material: 21 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 765-771 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 8 Ill.
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  • 6
    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.
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  • 7
    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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  • 8
    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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  • 9
    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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  • 10
    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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