Approximation Schemes for Monotone Systems of Nonlinear Second Order Partial Differential Equations : Convergence Result and Error Estimate

@inproceedings{Briani2011ApproximationSF,
  title={Approximation Schemes for Monotone Systems of Nonlinear Second Order Partial Differential Equations : Convergence Result and Error Estimate},
  author={Ariela Briani and Fabio Camilli and Hasnaa Zidani},
  year={2011}
}
We consider approximation schemes for monotone systems of fully nonlinear second order partial differential equations. We first prove a general convergence result for monotone, consistent and regular schemes. This result is a generalization to the well known framework of Barles-Souganidis, in the case of scalar nonlinear equation. Our second main result provides the convergence rate of approximation schemes for weakly coupled systems of Hamilton-Jacobi-Bellman equations. Examples including… CONTINUE READING