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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 29 (1978), S. 451-462 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30, 49D20 ; CR: 5.17, 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Nonlinear locally coercive variational inequalities are considered and especially the minimal surface over an obstacle. Optimal or nearly optimal error estimates are proved for a direct discretization of the problem with linear finite elements on a regular triangulation of the not necessarily convex domain. It is shown that the solution may be computed by a globally convergent relaxation method. Some numerical results are presented.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 35 (1980), S. 277-291 
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65N30 ; 65H10 ; 65K10 ; CR: 5.17, 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary On the efficient solution of nonlinear finite element equations. A fast numerical method is presented for the solution of nonlinear algebraic systems which arise from discretizations of elliptic boundary value problems. A simplified relaxation algorithm which needs no information about the Jacobian of the system is combined with a correspondingly modified conjugate gradient method. A global convergence proof is given and the number of operations required is compared with that of other algorithms which are equally applicable to a large class of problems. Numerical results verify the efficiency for some typical examples.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 36 (1981), S. 375-387 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30, 65K10, 49D20 ; CR: 5.17, 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider nonlinear variational inequalities corresponding to a locally convex minimization problem with linear constraints of obstacle type. An efficient method for the solution of the discretized problem is obtained by combining a slightly modified projected SOR-Newton method with the projected version of thec g-accelerated relaxation method presented in a preceding paper. The first algorithm is used to approximately reach in relatively few steps the proper subspace of active constraints. In the second phase a Kuhn-Tucker point is found to prescribed accuracy. Global convergence is proved and some numerical results are presented.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Computational optimization and applications 16 (2000), S. 29-55 
    ISSN: 1573-2894
    Keywords: elliptic control problems ; boundary control ; control and state constraints ; discretization techniques ; interior point optimization methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We study optimal control problems for semilinear elliptic equations subject to control and state inequality constraints. In a first part we consider boundary control problems with either Dirichlet or Neumann conditions. By introducing suitable discretization schemes, the control problem is transcribed into a nonlinear programming problem. It is shown that a recently developed interior point method is able to solve these problems even for high discretizations. Several numerical examples with Dirichlet and Neumann boundary conditions are provided that illustrate the performance of the algorithm for different types of controls including bang-bang and singular controls. The necessary conditions of optimality are checked numerically in the presence of active control and state constraints.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 95-104 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we generalize recent theoretical results on the local continuation of parameter-dependent non-linear variational inequalities. The variational inequalities are rather general and describe, for example, the buckling of beams, plates or shells subject to obstacles. Under a technical hypothesis that is satisfied by the simply supported beam, we obtain the existence of a continuation of both the solution and the eigenvalue with respect to a local parameter. A numerical continuation method is presented that easily overcomes turning points. Numerical results are presented for the non-linear beam.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 129-138 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the recent paper [13] we have answered the question of stability for the linear circular plate which is being axially compressed by a force greater than the critical value and contacts a plane obstacle. In this case there are radially symmetric solutions and the contact region is a disk of a smaller radius. This simplified the determination of the critical parameter values for which the plane jumps to another state. For the rectangular plate continuation has to be applied to the variational inequality in order to determine the contact region and evalute the stability criterion. A numerical method is developed for a discretization of the problem and is used to compute the critical load both in the simply supported and the clamped case.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Numerical algorithms 23 (2000), S. 315-328 
    ISSN: 1572-9265
    Keywords: interpolation ; rational interpolation ; optimal interpolation ; 65D05 ; 41A05 ; 41A20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract After recalling some pitfalls of polynomial interpolation (in particular, slopes limited by Markov's inequality) and rational interpolation (e.g., unattainable points, poles in the interpolation interval, erratic behavior of the error for small numbers of nodes), we suggest an alternative for the case when the function to be interpolated is known everywhere, not just at the nodes. The method consists in replacing the interpolating polynomial with a rational interpolant whose poles are all prescribed, written in its barycentric form as in [4], and optimizing the placement of the poles in such a way as to minimize a chosen norm of the error.
    Type of Medium: Electronic Resource
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  • 8
    Title: Numerical methods for bifurcation problems; 70
    Contributer: Küpper, Tassilo , Mittelmann, Hans D. , Weber, Helmut
    Publisher: Basel u.a. :Birkhäuser,
    Year of publication: 1984
    Pages: 584 S.
    Series Statement: Internationale Schriftenreihe zur numerischen Mathematik 70
    Type of Medium: Book
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  • 9
    Title: Continuation techniques and bifurcation problems; Vol. 92
    Contributer: Mittelmann, Hans D. , Roose, Dirk
    Publisher: Basel u.a. :Birkhäuser,
    Year of publication: 1990
    Pages: 218 S.
    Series Statement: International series of numerical mathematics Vol. 92
    Type of Medium: Book
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  • 10
    Publication Date: 2022-03-14
    Language: English
    Type: article , doc-type:article
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