Approximation schemes for monotone systems of nonlinear second order partial differential equations: convergence result and error estimate (Q2896911)

Approximation schemes for a system of fully nonlinear second-order partial differential equations are studied. In the first part of the paper, the authors recall some definitions and basic results for the continuous problem. Next, the main assumptions for the scheme are stated, and the convergence theorem is proved, which is the first main result of this paper. The second main result provides the convergence rate of approximation schemes for weakly coupled systems of Hamilton-Jacobi-Bellman equations. Examples include finite difference schemes and semi-Lagrangian schemes.