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

  title={A nonconforming Morley finite element method for the fully nonlinear Monge-Amp{\`e}re equation},
  author={Michael Neilan},
  journal={Numerische Mathematik},
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


Publications citing this paper.


Publications referenced by this paper.
Showing 1-10 of 26 references

Numerical Methods for Second Order Fully Nonlinear Partial Differential Equations

  • M. Neilan
  • PhD thesis, The University of Tennessee…
  • 2009
2 Excerpts

and L

  • S. C. Brenne
  • R. Scott, The Mathematical Theory of Finite…
  • 2008

Numerical methods for fully nonlinear elliptic equations of the Monge-Ampère type, Comput

  • E. J. Dean, R. Glowinski
  • Methods Appl. Mech. Engrg., 195(13-16):1344–1386,
  • 2006

Similar Papers

Loading similar papers…