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  • 1
    Electronic Resource
    Electronic Resource
    An acceleration method for integral equations by using interpolation post-processing (1998)
    Springer
    Advances in computational mathematics 9 (1998), S. 117-129 
    Details
    ISSN: 1572-9044
    Keywords: integral equations ; interpolation post-processing ; superconvergence ; Richardson extrapolation ; defect correction ; 65R20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Two post-processing techniques are widely used in the literature in the context of convergence acceleration. One of them is an interpolation technique, used for partial differential equations and integral differential equations, and the other is an iteration technique used for integral equations. These two techniques, interpolation and iteration, are quite different, and the former is simpler. Can we use the interpolation technique for integral equations instead of using the second iteration technique? This report gives a positive answer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018925103993
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A hybrid nonoverlapping domain decomposition scheme for advection dominated advection–diffusion problems (1998)
    Springer
    Numerical algorithms 18 (1998), S. 321-336 
    Details
    ISSN: 1572-9265
    Keywords: advection dominated problem ; domain decomposition ; 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Two nonoverlapping domain decomposition algorithms are proposed for convection dominated convection–diffusion problems. In each subdomain, artificial boundary conditions are used on the inflow and outflow boundaries. If the flow is simple, each subdomain problem only needs to be solved once. If there are closed streamlines, an iterative algorithm is needed and the convergence is proved. Analysis and numerical tests reveal that the methods are advantageous when the diffusion parameter ɛ is small. In such cases, the error introduced by the domain decomposition methods is negligible in comparison with the error in the singular layers, and it allows easy and efficient grid refinement in the singular layers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019133818553
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A Posteriori Error Estimators for a Class of Variational Inequalities (2000)
    Springer
    Journal of scientific computing 15 (2000), S. 361-393 
    Details
    ISSN: 1573-7691
    Keywords: finite element approximation ; variational inequalities ; a posteriori error estimators ; obstacle problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In this paper, we present an a posteriori error analysis for the finite element approximation of a variational inequality. We derive a posteriori error estimators of residual type, which are shown to provide upper bounds on the discretization error for a class of variational inequalities provided the solutions are sufficiently regular. Furthermore we derive sharp a posteriori error estimators with both lower and upper error bounds for a subclass of the obstacle problem which are frequently met in many physical models. For sufficiently regular solutions, these estimates are shown to be equivalent to the discretization error in an energy type norm. Our numerical tests show that these sharp error estimators are both reliable and efficient in guiding mesh adaptivity for computing the free boundaries.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1011130501691
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    A finite element method for evaluating a double integral arising from a Dirichlet problem in fluid mechanics (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 627-634 
    Details
    ISSN: 1069-8299
    Keywords: finite elements ; doubly connected regions ; Poisson's equation ; viscous flow ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we give a finite element method and its error estimate for evaluating double integrals over a smooth domain. The results are used to compare rates of flow of a viscous incompressible fluid in a pipe-in-pipe system with different doubly connected cross-sections. These numerical results confirm an earlier conjecture regarding the rates of flow. ©1997 John Wiley & Sons, Ltd.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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