Singular Perturbation Problems

  • Wolfgang Hackbusch
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 4)


An operator L = L(ε) depending on a parameter ε is called singularly perturbed if the limiting operator \(L(0) = \begin{array}{*{20}{c}} {\lim } \\ {\varepsilon \to 0} \end{array}L(\varepsilon )\) is of a type other than L(ε) for ε > 0. For instance, an elliptic operator L(ε) = ε L I + L II (ε > 0) is singularly perturbed if L II is non-elliptic or elliptic of a lower order. Different types of L II give rise to the subsections 10.1–3.


Finite Element Discretisation Convection Diffusion Equation Singular Perturbation Problem Smoothing Process Multigrid Iteration 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Wolfgang Hackbusch
    • 1
  1. 1.MPI für Mathematik in den NaturwissenschaftenLeipzigGermany

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