Local Defect Correction Method and Domain Decomposition Techniques

  • W. Hackbusch
Part of the Computing Supplementum book series (COMPUTING, volume 5)


For elliptic problems a local defect correction method is described. A basic (global) discretization is improved by a local discretization defined in a subdomain. The convergence rate of the local defect correction iteration is proved to be proportional to a certain positive power of the step size. The accuracy of the converged solution can be described. Numerical examples confirm the theoretical results. We discuss multi-grid iterations converging to the same solution.

The local defect correction determines a solution depending on one global and one or more local discretizations. An extension of this approach is the domain decomposition method, where only (overlapping) local problems are combined. Such a combination of local subproblems can be solved efficiently by a multi-grid iteration. We describe a multi-grid variant that is suited for the use of parallel processors.


Local Problem Domain Decomposition Multigrid Method Domain Decomposition Method Interior Boundary 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • W. Hackbusch
    • 1
  1. 1.Institut für Informatik und Praktische MathematikChristian-Albrechts-UniversitätKiel 1Federal Republic of Germany

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