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  • Articles  (43)
  • AMS(MOS): 65N30  (25)
  • nonlinear programming  (16)
  • Ecology
  • crystal structure
  • 1980-1984  (43)
  • Mathematics  (42)
  • Geosciences  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Maximum-norm stability and error estimates in Galerkin methods for parabolic equations in one space variable (1983)
    Springer
    Numerische Mathematik 41 (1983), S. 345-371 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Maximum-norm stability and error estimates of best approximation and nonsmooth data types are derived for the approximate solution of a parabolic equation in one space variable, using the continuous in time Galerkin method based on piecewise polynomial approximating functions on a quasi-uniform mesh.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01418330
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  • 2
    Electronic Resource
    Electronic Resource
    A mixed finite element approximation of the Navier-Stokes equations (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 381-404 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We study in this paper the convergence of a new mixed finite element approximation of the Navier-Stokes equations. This approximation uses low order Lagrange elements, leads to optimal order of convergence for the velocity and the pressure, and induces an efficient numerical algorithm for the solution of this problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399007
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  • 3
    Electronic Resource
    Electronic Resource
    A convergence condition for the quadrilateral Wilson element (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 349-361 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G 1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The paper deals with the convergence properties of the nonconforming quadrilateral wilson element which violates the patch test. The convergence of the element is proved under a certain condition on mesh subdivisions without any modifications of the variational formulation. This result extends the range of applicability of Wilson's element. The necessity of the proposed condition is also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01405567
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  • 4
    Electronic Resource
    Electronic Resource
    Approximation de quelques problèmes de type Stokes par une méthode d'éléments finis mixtes (1984)
    Springer
    Numerische Mathematik 45 (1984), S. 75-91 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5-17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Summary We present in this paper a mixed-finite element approximation of Stokes equations with boundary conditions of Fourier's or Neumann's type. For this approximation we prove that the error estimates for the velocity-vector and for the pressure are optimal. These results of convergence generalize to this kind of boundary conditions the Glowinski-Pironneau's approximation of Stokes problem with Dirichlet's boundary conditions [9, 10].
    Notes: Résumé Nous présentons dans cet article une méthode d'éléments finis mixtes qui permet la résolution des équations de Stokes avec des conditions aux limites de type Fourier ou Neumann. Pour cette méthode nous démontrons que les estimations de l'erreur d'approximation sont optimales; en vitesse et en pression. Ces résultats de convergences généralisent à ce type non standard de conditions aux limites les travaux de Glowinski-Pironneau [9, 10] pour le probleme de Stokes avec des conditions aux limites de Dirichlet.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01379662
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  • 5
    Electronic Resource
    Electronic Resource
    Estimations des erreurs de meilleure approximation polynomiale et d'interpolation de Lagrange dans les espaces de Sobolev d'ordre non entier (1984)
    Springer
    Numerische Mathematik 45 (1984), S. 301-321 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G18
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Summary Explicit bounds for the best polynomial approximation error, explicit and non-explicit bounds for the Lagrange interpolation error are derived for functions belonging to fractional order Sobolev spaces defined over a bounded open set in ℝ n . Thus the classical results of the integer order Sobolev spaces are extended.
    Notes: Résumé On établit des majorations explicites de I'erreur de meilleure approximation polynomiale ainsi que des majorations explicites et nonexplicites de I'erreur d'interpolation de Lagrange, lorsque la fonction considérée appartient à un espace de Sobolev d'ordre non entier défini sur un ouvert borné de ℝ n . Les résultats obtenus généralisent les résultats connus dans le cas des espaces de Sobolev d'ordre entier.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389473
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  • 6
    Electronic Resource
    Electronic Resource
    Error estimates for the combinedh andp versions of the finite element method (1981)
    Springer
    Numerische Mathematik 37 (1981), S. 257-277 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In theh-version of the finite element method, convergence is achieved by refining the mesh while keeping the degree of the elements fixed. On the other hand, thep-version keeps the mesh fixed and increases the degree of the elements. In this paper, we prove estimates showing the simultaneous dependence of the order of approximation on both the element degrees and the mesh. In addition, it is shown that a proper design of the mesh and distribution of element degrees lead to a better than polynomial rate of convergence with respect to the number of degrees of freedom, even in the presence of corner singularities. Numerical results comparing theh-version,p-version, and combinedh-p-version for a one dimensional problem are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398256
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  • 7
    Electronic Resource
    Electronic Resource
    A globally convergent, implementable multiplier method with automatic penalty limitation (1980)
    Springer
    Applied mathematics & optimization 6 (1980), S. 335-360 
    Details
    ISSN: 1432-0606
    Keywords: nonlinear programming ; multiplier methods ; penalty methods ; global convergence ; penalty limitation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with penalty function and multiplier methods for the solution of constrained nonconvex nonlinear programming problems. Starting from an idea introduced several years ago by Polak, we develop a class of implementable methods which, under suitable assumptions, produce a sequence of points converging to a strong local minimum for the problem, regardless of the location of the initial guess. In addition, for sequential minimization type multiplier methods, we make use of a rate of convergence result due to Bertsekas and Polyak, to develop a test for limiting the growth of the penalty parameter and thereby prevent ill-conditioning in the resulting sequence of unconstrained optimization problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01442901
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  • 8
    Electronic Resource
    Electronic Resource
    The finite element method for parabolic equations (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 339-371 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; 65M20 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this first of two papers, computable a posteriori estimates of the space discretization error in the finite element method of lines solution of parabolic equations are analyzed for time-independent space meshes. The effectiveness of the error estimator is related to conditions on the solution regularity, mesh family type, and asymptotic range for the mesh size. For clarity the results are limited to a model problem in which piecewise linear elements in one space dimension are used. The results extend straight-forwardly to systems of equations and higher order elements in one space dimension, while the higher dimensional case requires additional considerations. The theory presented here provides the basis for the analysis and adaptive construction of time-dependent space meshes, which is the subject of the second paper. Computational results show that the approach is practically very effective and suggest that it can be used for solving more general problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396451
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  • 9
    Electronic Resource
    Electronic Resource
    Error analysis for Laplace transform —Finite element solution of hyperbolic equations (1983)
    Springer
    Numerische Mathematik 41 (1983), S. 55-62 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The finite element method with Laplace transform of time variable is proposed for the solution of hyperbolic equations. Error estimates in Hardy spaces of functions with values in Sobolev spaces are derived. Due to the isometric isomorphism of Hardy spaces with weighted Hilbert spaces these estimates are valid also for original formulations of hyperbolic equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396305
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  • 10
    Electronic Resource
    Electronic Resource
    An analysis of thep-version of the finite element method for nearly incompressible materials (1983)
    Springer
    Numerische Mathematik 41 (1983), S. 39-53 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; 73K25 CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we analyze the behavior of the so-calledp-version of the finite element method when applied to the equations of plane strain linear elasticity. We establish optimal rate error estimates that are uniformly valid, independent of the value of the Poisson ratio,v, in the interval ]0, 1/2[. This shows that thep-versiondoes not exhibit the degeneracy phenomenon which has led to the use of various, only partially justified techniques of reduced integration or mixed formulations for more standard finite element schemes and the case of a nearly incompressible material.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396304
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