• Corpus ID: 239616164

Adaptive FEM for Helmholtz Equation with Large Wave Number

@article{Duan2021AdaptiveFF,
  title={Adaptive FEM for Helmholtz Equation with Large Wave Number},
  author={Songyao Duan and Haijun Wu},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.11939}
}
A posteriori upper and lower bounds are derived for the linear finite element method (FEM) for the Helmholtz equation with large wave number. It is proved rigorously that the standard residual type error estimator seriously underestimates the true error of the FE solution for the mesh size h in the preasymptotic regime, which is first observed by Babuška, et al. for an one dimensional problem. By establishing an equivalence relationship between the error estimators for the FE solution and the… 

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