On Standard Finite Difference Discretizations of the Elliptic Monge–Ampère Equation

@article{Awanou2016OnSF,
  title={On Standard Finite Difference Discretizations of the Elliptic Monge–Amp{\`e}re Equation},
  author={Gerard Awanou},
  journal={Journal of Scientific Computing},
  year={2016},
  volume={69},
  pages={892-904}
}
  • Gerard Awanou
  • Published 2016
  • Mathematics, Computer Science
  • Journal of Scientific Computing
Given an orthogonal lattice with mesh length h on a bounded two-dimensional convex domain $${\varOmega }$$Ω, we propose to approximate the Aleksandrov solution of the Monge–Ampère equation by regularizing the data and discretizing the equation in a subdomain using the standard finite difference method. The Dirichlet data is used to approximate the solution in the remaining part of the domain. We prove the uniform convergence on compact subsets of the solution of the discrete problems to an… Expand
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