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  • AMS(MOS): 65F10  (2)
  • CR: 5.17  (2)
  • AMS: 65L05  (1)
  • 1
    Digitale Medien
    Digitale Medien
    The hierarchical basis multigrid method (1988)
    Springer
    Numerische Mathematik 52 (1988), S. 427-458 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65F10 ; 65F35 ; 65N20 ; 65N30 ; CR:G1.8
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We derive and analyze the hierarchical basis-multigrid method for solving discretizations of self-adjoint, elliptic boundary value problems using piecewise linear triangular finite elements. The method is analyzed as a block symmetric Gauß-Seidel iteration with inner iterations, but it is strongly related to 2-level methods, to the standard multigridV-cycle, and to earlier Jacobi-like hierarchical basis methods. The method is very robust, and has a nearly optimal convergence rate and work estimate. It is especially well suited to difficult problems with rough solutions, discretized using highly nonuniform, adaptively refined meshes.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01462238
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  • 2
    Digitale Medien
    Digitale Medien
    A class of iterative methods for solving saddle point problems (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 645-666 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65F10 ; 65N20 ; 65N30 ; CR: G 1.8
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We consider the numerical solution of indefinite systems of linear equations arising in the calculation of saddle points. We are mainly concerned with sparse systems of this type resulting from certain discretizations of partial differential equations. We present an iterative method involving two levels of iteration, similar in some respects to the Uzawa algorithm. We relate the rates of convergence of the outer and inner iterations, proving that, under natural hypotheses, the outer iteration achieves the rate of convergence of the inner iteration. The technique is applied to finite element approximations of the Stokes equations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01405194
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  • 3
    Digitale Medien
    Digitale Medien
    Die gleichmäßige Stabilität singulär gestörter diskreter und kontinuierlicher Randwertprobleme (1983)
    Springer
    Numerische Mathematik 41 (1983), S. 223-253 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS: 65L05 ; 65L10 ; 34D15 CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary In this paper we consider singular perturbation problems for ordinary differential operators of ordern and their discrete counterparts on arbitrary nonuniform grids. We prove that the singularly perturbed initial value problem is stable uniformly in the perturbation parameter ε in both the continuous and the discrete case. We use this result to characterize the stability of the corresponding continuous and discrete boundary value problems. If the continuous problem is stable and if the consistency error is smaller than a certain constant, the discrete problem is also stable.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01390214
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  • 4
    Digitale Medien
    Digitale Medien
    Die maximale Konsistenzordnung von Differenzenapproximationen nichtnegativer Art (1983)
    Springer
    Numerische Mathematik 42 (1983), S. 119-123 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N10 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Many difference methods for the numerical solution of elliptic boundary value problems lead to systems of linear equations whose matrices areM-matrices and which therefore have nonnegative inverses. In this paper it is shown, that these difference methods are at most consistent of second order.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01400922
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  • 5
    Digitale Medien
    Digitale Medien
    Die mehrstellenformeln für den Laplaceoperator (1980)
    Springer
    Numerische Mathematik 34 (1980), S. 171-187 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N05 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Difference methods for the numerical solution of linear partial differential equations may often be improved by using a weighted right hand side instead of the original right hand side of the differential equation. Difference formulas, for which that is possible, are called “Mehrstellenformeln’ or Hermitian formulas. In this paper the Hermitian formulas for the approximation of Laplace's operator are characterized by a very simple condition. We prove, that in two-dimensional case for a Hermitian formula of ordern at leastn+3 discretization points are necessary. We give examples of such optimal formulas of arbitrary high-order.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01396058
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