We propose a new splitting algorithm to solve a class of quasilinear PDEs with convex and quadratic growth gradients.
By splitting the original equation into a linear parabolic equation and a Hamilton-Jacobi equation, we are able to solve both equations explicitly.
In particular, we solve the associated Hamilton-Jacobi equation by the Hopf-Lax formula,
and interpret the splitting algorithm as a stochastic Hopf-Lax approximation of the quasilinear PDE.
We show that the numerical solution will converge to the viscosity solution of the equation.
The upper bound of the convergence rate is proved based on Krylov's shaking coefficients technique,
while the lower bound is proved based on Barles-Jakobsen's optimal switching approximation technique.
Based on joint work with Shuo Huang and Thaleia Zariphopoulou.