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  • 1
    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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  • 2
    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
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
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