Pseudo transient continuation and time marching methods for Monge-Ampère type equations

@article{Awanou2015PseudoTC,
  title={Pseudo transient continuation and time marching methods for Monge-Amp{\`e}re type equations},
  author={Gerard Awanou},
  journal={Adv. Comput. Math.},
  year={2015},
  volume={41},
  pages={907-935}
}
We present two numerical methods for the fully nonlinear elliptic MongeAmpère equation. The first is a pseudo transient continuation method and the second is a pure pseudo time marching method. The methods are proved to converge for smooth solutions. We give numerical evidence that they are also able to capture the viscosity solution of the Monge-Ampère equation. Even in the case of the degenerate Monge-Ampère equation, the time marching method appears also to compute the viscosity solution.