Finite element approximations in a non-Lipschitz domain: Part II

@article{Acosta2011FiniteEA,
  title={Finite element approximations in a non-Lipschitz domain: Part II},
  author={Gabriel Acosta and Mar{\'i}a G. Armentano},
  journal={Math. Comput.},
  year={2011},
  volume={80},
  pages={1949-1978}
}
In a paper by R. Durán, A. Lombardi, and the authors (2007) the finite element method was applied to a non-homogeneous Neumann problem on a cuspidal domain Ω ⊂ R2, and quasi-optimal order error estimates in the energy norm were obtained for certain graded meshes. In this paper, we study the error in the L2 norm obtaining similar results by using graded meshes of the type considered in that paper. Since many classical results in the theory Sobolev spaces do not apply to the domain under… CONTINUE READING

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Finite element approximations in a non-Lipschitz domain

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