A nonconforming Morley finite element method for the fully nonlinear Monge-Ampère equation

@article{Neilan2010ANM,
  title={A nonconforming Morley finite element method for the fully nonlinear Monge-Amp{\`e}re equation},
  author={Michael Neilan},
  journal={Numerische Mathematik},
  year={2010},
  volume={115},
  pages={371-394}
}
In this paper, we study finite element approximations of the viscosity solution of the fully nonlinear Monge-Ampère equation, det(Du) = f (> 0) using the well-known nonconforming Morley element. Our approach is based on the vanishing moment method, which was recently proposed as a constructive way to approximate fully nonlinear second order equations by the author and Feng in [15]. The vanishing moment method approximates the Monge-Ampère equation by the fourth order quasilinear equation − ∆u… CONTINUE READING

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