Time permitting, we will discuss two topics. First, we will discuss a semicoarsening multigrid method for the solution of vertex-centered systems. Second, we will discuss a new method for the solution of the system arising in the Morel diffusion scheme. In this system, unknowns reside at cell centers and cell edges of a quadrilateral mesh. We will also discuss the solution of a new difference scheme on such meshes due to Morel and Shashkov.