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  • 1
    Electronic Resource
    Electronic Resource
    On the approximate solution of nonlinear variational inequalities (1978)
    Springer
    Numerische Mathematik 29 (1978), S. 451-462 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF01432881
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the efficient solution of nonlinear finite element equations I (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 277-291 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF01396413
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    On the efficient solution of nonlinear finite element equations. II (1981)
    Springer
    Numerische Mathematik 36 (1981), S. 375-387 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF01395953
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    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
    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
    URL: http://dx.doi.org/10.1023/A:1019168504808
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    Paper (German National Licenses)
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