In this presentation, we focus on stationary first-order Hamilton-Jacobi equations with arbitrary two-dimensional domains. Our aim is to implement a finite-difference scheme that satisfies monotonicity, consistency, and stability properties. Due to the Barles-Souganidis result, the scheme locally uniformly converges to a unique viscosity solution of the Hamilton-Jacobi equation. To solve the scheme numerically, we use the Euler map with some initial guess. We illustrate our numerical results in several examples.