Nonlinear elliptic and parabolic partial differential equations (PDEs)
appear in problems from science, engineering, atmospheric/ocean studies,
image processesing, and mathematical finance.

The theory of viscosity solutions has been enormously successful
in addressing the problems of existence, uniqueness,
and stability for a wide class of such equations.

A problem which has not been addressed with as much success
is the construction of solutions. In some cases,
exact solutions formulas exist, but for the most part,
solutions must be found numerically.

In the past schemes for first order equation were built by exploiting
the connection with conservation laws.
Building schemes for second order equations was more of a challenge.

We introduce a framework for building monotone schemes which converge
to the viscosity solution.
This framework allows explicit nonlinear finite difference schemes to
be built.

We will present convergent schemes and computational results for:
level set motion by mean curvature, the convex hull, the infinity
Laplacian, the Monge-Ampere equation, and other equations.