EFFICIENT PARAMETERS OF DECOUPLED DUAL SINGULAR FUNCTION METHOD

  • Kim, Seok-Chan (DEPARTMENT OF APPLIED MATHEMATICS, CHANGWON NATIONAL UNIVERSITY) ;
  • Pyo, Jae-Hong (DEPARTMENT OF MATHEMATICS, KANGWON NATIONAL UNIVERSITY)
  • Received : 2009.09.25
  • Accepted : 2009.11.18
  • Published : 2009.12.25

Abstract

The solution of the interface problem or Poisson problem with concave corner has singular perturbation at the interface corners or singular corners. The decoupled dual singular function method (DDSFM) which exploits the singular representations of the solutions was suggested in [3, 9] and estimated optimal accuracy in [10]. The convergence rates consist with theoretical results even for the problems with very strong singularity, with the efficiency depending on parameters used in the methods. Furthermore the errors in $L^2$ and $L^\infty$-spaces display some oscillation, in the cases with meshsize not small enough. In this paper, we present an answer to remove the oscillation via numerical experiments. We observe the effects of parameters in DDSFM, and show the consisting efficiency of the method over the strong singularity.

Acknowledgement

Supported by : National Research Foundation, Korea Research Foundation

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