Quadtrees Mesh

This repo contains code for the paper Higher-order Adaptive Finite Difference Methods for Fully Nonlinear Elliptic Equations.

Code

The script example_meshes.m illustrates the wide range of different meshes that can be created. It displays the following meshes.

The script example_MA.m contains an example on how to call the solvers for the Monge-Ampere equation with both the monotone scheme and the filtered scheme.

The script example_ConEnv.m contains an example on how to call the solvers for the Convex Envelope equation with both the standard mesh and and a refined mesh.

Citation

If you use this paper or code in your scientific work, please cite as

@article{MeshFreeHamfeldtSalvador,
  title     = {Higher-order adaptive finite difference methods for fully nonlinear elliptic equations},
  author    = {Hamfeldt, Brittany Froese and Salvador, Tiago},
  journal   = {Journal of Scientific Computing},
  volume    = {75},
  number    = {3},
  pages     = {1282--1306},
  year      = {2018},
  publisher = {Springer}
}