Convergence of a Numerical Scheme for the Hamilton-Jacobi Equation: a   New Approach with the Adjoint Method
  We consider a numerical scheme for the one dimensional time dependent Hamilton-Jacobi equation in the periodic setting. We present a new and simple proof of the rate of convergence of the approximations based on the adjoint method recently introduced by Evans. 
Filippo Cagnetti, Diogo Gomes, and Hung V. Tran
math.AP math.NA