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  • Articles  (133)
  • CR: G1.8  (133)
  • Mathematics  (133)
  • 1
    Electronic Resource
    Electronic Resource
    L ∞-Error estimate for an approximation of a parabolic variational inequality (1987)
    Springer
    Numerische Mathematik 50 (1987), S. 557-565 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Almost optimalL ∞-convergence of an approximation of a variational inequality of parabolic type is proved under regularity assumptions which are met by the solution of a one phase Stefan problem. The discretization employs piecewise linear finite elements in space and the backward Euler scheme in time. By means of a maximum principle the problem is reduced to an error estimate for an auxiliary parabolic equation. The latter bound is obtained by using the smoothing property of the Galerkin method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01408576
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  • 2
    Electronic Resource
    Electronic Resource
    Numerical solution for exterior problems (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 87-101 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We solve the Helmholtz equation in an exterior domain in the plane. A perfect absorption condition is introduced on a circle which contains the obstacle. This boundary condition is given explicitly by Bessel functions. We use a finite element method in the bounded domain. An explicit formula is used to compute the solution out of the circle. We give an error estimate and we present relevant numerical results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399696
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  • 3
    Electronic Resource
    Electronic Resource
    Mixed finite elements for second order elliptic problems in three variables (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 237-250 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Two families of mixed finite elements, one based on simplices and the other on cubes, are introduced as alternatives to the usual Raviart-Thomas-Nedelec spaces. These spaces are analogues of those introduced by Brezzi, Douglas, and Marini in two space variables. Error estimates inL 2 andH −s are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396752
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  • 4
    Electronic Resource
    Electronic Resource
    Error analysis for absorbing boundary conditions (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 459-467 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 35L20 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary An estimate is derived for the error committed by the introduction of artificial boundaries and corresponding artificial boundary conditions when solving wave equations on unbounded domains. The estimate has two terms. One is proportional to the largest reflection coefficient for the artificial boundary condition, the maximum taken only on those rays which appear in the computation. The second term is proportional to 1/k wherek is a measure of the average frequency present in the solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397547
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  • 5
    Electronic Resource
    Electronic Resource
    On the numerical approximation of finite speed diffusion problems (1988)
    Springer
    Numerische Mathematik 53 (1988), S. 97-105 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Lagrangian formulations for the Cauchy problems for the generalized-heat and porous-media equations are introduced and equivalence and existence results discussed. Efficient interface tracking finite difference and finite element discretizations of the Lagrangian formulation are discussed. Mixed Euler-Lagrange formulations for mixed problems and the one phase Stefan problem are presented. Numerical experiments are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395879
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  • 6
    Electronic Resource
    Electronic Resource
    Convergence of the multilevel Full Approximation Scheme including theV-cycle (1988)
    Springer
    Numerische Mathematik 53 (1988), S. 663-686 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N20 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The multilevel Full Approximation Scheme (FAS ML) is a well-known solver for nonlinear boundary value problems. In this paper we prove local quantitative convergence statements for a class of FAS ML algorithms in a general Hilbertspace setting. This setting clearly exhibits the structure of FAS ML. We prove local convergence of a nested iteration for a rather concrete class of FAS ML algorithms in whichV-cycles and only one Jacobilike pre- and post-smoothing on each level are used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397135
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  • 7
    Electronic Resource
    Electronic Resource
    Control of stefan problems by means of linear-quadratic defect minimization (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 429-442 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65P05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We investigate the following problem: To influence a heat conduction process in such a way that the conductor melts in a prescribed manner. Since we treat a linear auxiliary problem, it suffices to deal with a linear-quadratic defect minimization problem with linear restrictions, where we use splines or polynomials as approximation spaces. In case of exact controllability we derive various order of convergence estimates, which we discuss for some numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389495
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  • 8
    Electronic Resource
    Electronic Resource
    A finite element lumped mass scheme for solving eigenvalue problems of circular arches (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 499-504 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This study is a continuation of a previous paper [4] in which the numerical results are given by using single precision arithmetic. In this paper, we show the numerical results which experess the sharper convergence properties than those of [4], by using double precision arithmetic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389655
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  • 9
    Electronic Resource
    Electronic Resource
    Finite element approximation of viscoelastic progressively incompressible flows (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 43-66 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65K19 ; 65N30 ; 73F05 ; 76A05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary To avoid any numerical locking in the finite element approximation of viscoelastic flow problems, we propose a three-field approximation of this problem. This approximation, which involves velocities, stresses, and pressures is proved to converge for all times. In the proof, we also obtain convergence results for the three-fields finite element approximation of incompressible elasticity problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395777
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  • 10
    Electronic Resource
    Electronic Resource
    Spectral methods with sparse matrices (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 25-41 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N35 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Spectral methods employ global polynomials for approximation. Hence they give very accurate approximations for smooth solutions. Unfortunately, for Dirichlet problems the matrices involved are dense and have condition numbers growing asO(N 4) for polynomials of degree ≦N in each variable. We propose a new spectral method for the Helmholtz equation with a symmetric and sparse matrix whose condition number grows only asO(N 2). Certain “algebraic spectral multigrid methods” can be efficiently used for solving the resulting system. Numerical results are presented which show that we have probably found the most effective solver for spectral systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395776
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