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  • Digitale Medien  (3)
  • 2000-2004  (2)
  • 1975-1979  (1)
  • 1
    Digitale Medien
    Digitale Medien
    On the approximate solution of nonlinear variational inequalities (1978)
    Springer
    Numerische Mathematik 29 (1978), S. 451-462 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N30, 49D20 ; CR: 5.17, 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01432881
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  • 2
    Digitale Medien
    Digitale Medien
    Optimization Techniques for Solving Elliptic Control Problems with Control and State Constraints: Part 1. Boundary Control (2000)
    Springer
    Computational optimization and applications 16 (2000), S. 29-55 
    Details
    ISSN: 1573-2894
    Schlagwort(e): elliptic control problems ; boundary control ; control and state constraints ; discretization techniques ; interior point optimization methods
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008725519350
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  • 3
    Digitale Medien
    Digitale Medien
    Rational interpolation through the optimal attachment of poles to the interpolating polynomial (2000)
    Springer
    Numerical algorithms 23 (2000), S. 315-328 
    Details
    ISSN: 1572-9265
    Schlagwort(e): interpolation ; rational interpolation ; optimal interpolation ; 65D05 ; 41A05 ; 41A20
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1019168504808
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