The numerical methods for oscillating singularities in elliptic boundary value problems

@article{Oh2001TheNM,
  title={The numerical methods for oscillating singularities in elliptic boundary value problems},
  author={Hae-Soo Oh and Hoonjoo Kim and Sungjin Lee},
  journal={Journal of Computational Physics},
  year={2001},
  volume={170},
  pages={742-763}
}
The singularities near the crack tips of homogeneous materials are monotone of type rα and rα logδr (depending on the boundary conditions along nonsmooth domains). However, the singularities around the interfacial cracks of the heterogeneous bimaterials are oscillatory of type rα sin(e log r). The method of auxiliary mapping (MAM), introduced by Babuska and Oh, was proven to be successful in dealing with rα type singularities. However, the effectiveness of MAM is reduced in handling oscillating… 

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