Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems

@article{Douglas1999NonconformingGM,
  title={Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems},
  author={Jim Douglas and Juan E. Santos and Dongwoo Sheen and Xiu Ye},
  journal={Mathematical Modelling and Numerical Analysis},
  year={1999},
  volume={33},
  pages={747-770}
}
Low-order nonconforming Galerkin methods will be analyzed for second-order elliptic equations subjected to Robin, Dirichlet, or Neumann boundary conditions. Both simplicial and rectangular elements will be considered in two and three dimensions. The simplicial elements will be based on P 1 , as for conforming elements; however, it is necessary to introduce new elements in the rectangular case. Optimal order error estimates are demonstrated in all cases with respect to a broken norm in H 1… 
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