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  • Artikel  (99)
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  • AMS(MOS): 65N30  (57)
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  • 1
    Digitale Medien
    Digitale Medien
    Semi-iterative methods for the approximate solution of ill-posed problems (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 263-271 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65F10 ; CR: G1.3
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We study semi-iterative (two step interative) methods of the form $$x_{n + 1} = T^* T(\alpha x_n + \gamma x_{n - 1} ) + \beta x_n + (1 - \beta )x_{n - 1} - (\alpha + \gamma )T^* y$$ for the approximate solution of ill-posed or ill-conditioned linear equationsTx=y in (infinite or finite dimensional) Hilbert spaces. We present results on convergence, convergence rates, the influence of perturbed data, and on the comparison of different methods.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01390704
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  • 2
    Digitale Medien
    Digitale Medien
    Finite element approximation on incompressible Navier-Stokes equations with slip boundary condition (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 697-721 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N30 ; CR: G1.8
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We consider a mixed finite element approximation of the stationary, incompressible Navier-Stokes equations with slip boundary condition, which plays an important rôle in the simulation of flows with free surfaces and incompressible viscous flows at high angles of attack and high Reynold's numbers. The central point is a saddle-point formulation of the boundary conditions which avoids the well-known Babuška paradox when approximating smooth domains by polyhedrons. We prove that for the new formulation one can use any stable mixed finite element for the Navier-Stokes equations with no-slip boundary condition provided suitable bubble functions on the boundary are added to the velocity space. We obtain optimal error estimates under minimal regularity assumptions for the solution of the continous problem. The techniques apply as well to the more general Navier boundary condition.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01398380
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  • 3
    Digitale Medien
    Digitale Medien
    On the numerical treatment of viscous flows against bodies with corners and edges by boundary element and multigrid methods (1987)
    Springer
    Numerische Mathematik 52 (1987), S. 81-99 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N30 ; CR: G 1.8
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary The slow viscous flow past a spatial body with corners and edges is investigated mathematically and numerically by means of a boundary element method. For the resulting algebraic system a multigrid solver is designed and analyzed. Due to an improved bound on the rate of convergence it proves to be preferable to that introduced earlier for related problems. A numerical example illustrates some of the proposed methods.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01401023
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  • 4
    Digitale Medien
    Digitale Medien
    Compactness method in the finite element theory of nonlinear elliptic problems (1988)
    Springer
    Numerische Mathematik 52 (1988), S. 147-163 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N30 ; CR: G1.8
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Finite element approximation of a nonlinear elliptic pseudomonotone second-order boundary value problem in a bounded nonpolygonal domain Ω with mixed Dirichlet-Neumann boundary conditions is studied. In the discretization we approximate the domain Ω by a polygonal one, use linear conforming triangular elements and evaluate integrals by numerical quadratures. We prove the solvability of the discrete problem and on the basis of compactness properties of the corresponding operator (which is not monotone in general) we prove the convergence of approximate solutions to an exact weak solutionu∈H 1 Ω). No additional assumption on the regularity of the exact solution is needed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01398687
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  • 5
    Digitale Medien
    Digitale Medien
    Lower bounds for the condition number of Vandermonde matrices (1987)
    Springer
    Numerische Mathematik 52 (1987), S. 241-250 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS (MOS): 15A12 ; 49D15 ; 65F35 ; CR: G1.3 ; G1.6
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We derive lower bounds for the ∞-condition number of then×n-Vandermonde matrixV n(x) in the cases where the node vectorx T=[x1, x2,...,xn] has positive elements or real elements located symmetrically with respect to the origin. The bounds obtained grow exponentially inn. withO(2n) andO(2n/2), respectively. We also compute the optimal spectral condition numbers ofV n(x) for the two node configurations (including the optimal nodes) and compare them with the bounds obtained.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01398878
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  • 6
    Digitale Medien
    Digitale Medien
    Rehabilitation of the Gauss-Jordan algorithm (1989)
    Springer
    Numerische Mathematik 54 (1989), S. 591-599 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65F05, 65G05, 15A06 ; CR: G1.3
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary In this paper a Gauss-Jordan algorithm with column interchanges is presented and analysed. We show that, in contrast with Gaussian elimination, the Gauss-Jordan algorithm has essentially differing properties when using column interchanges instead of row interchanges for improving the numerical stability. For solutions obtained by Gauss-Jordan with column interchanges, a more satisfactory bound for the residual norm can be given. The analysis gives theoretical evidence that the algorithm yields numerical solutions as good as those obtained by Gaussian elimination and that, in most practical situations, the residuals are equally small. This is confirmed by numerical experiments. Moreover, timing experiments on a Cyber 205 vector computer show that the algorithm presented has good vectorisation properties.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01396364
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  • 7
    Digitale Medien
    Digitale Medien
    Homotopy algorithm for symmetric eigenvalue problems (1989)
    Springer
    Numerische Mathematik 55 (1989), S. 265-280 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS) ; 65H10 ; 58C99 ; 55M25 ; CR: G1.3
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary The homotopy method can be used to solve eigenvalue-eigenvector problems. The purpose of this paper is to report the numerical experience of the homotopy method of computing eigenpairs for real symmetric tridiagonal matrices together with a couple of new theoretical results. In practice, it is rerely of any interest to compute all the eigenvalues. The homotopy method, having the order preserving property, can provide any specific eigenvalue without calculating any other eigenvalues. Besides this advantage, we note that the homotopy algorithm is to a large degree a parallel algorithm. Numerical experimentation shows that the homotopy method can be very efficient especially for graded matrices.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01390054
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  • 8
    Digitale Medien
    Digitale Medien
    L ∞-Error estimate for an approximation of a parabolic variational inequality (1987)
    Springer
    Numerische Mathematik 50 (1987), S. 557-565 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N30 ; CR: G1.8
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01408576
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  • 9
    Digitale Medien
    Digitale Medien
    Numerical solution for exterior problems (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 87-101 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N30 ; CR: G1.8
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01399696
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  • 10
    Digitale Medien
    Digitale Medien
    Mixed finite elements for second order elliptic problems in three variables (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 237-250 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N30 ; CR: G1.8
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01396752
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