I will define and analyze a mixed DG, convex splitting scheme for a modified Cahn-Hilliard equation. The equation represents a diffuse interface model for phase separation in diblock coploymer blends and permits rather exotic solutions compared to the classical Cahn-Hilliard equation, including solutions like those from the phase field crystal model. The talk will cover theoretical energy stability and convergence results and also the practical, efficient solution of the algebraic equations via an adaptive nonlinear multigrid method. This is joint work with A. Aristotelous (SAMSI) and O. Karakashian (UTK).