An unconditionally stable embedded discontinuous Galerkin method for the phase field crystal equation

The phase field crystal (PFC) is a partial differential equation that models the growth of crystals in a liquid at the atomic scale in space, and diffusive scale in time. Since the PFC equation is sixth order and nonlinear, its numerical discretization often requires expensive algorithms. Moreover, proving existence and uniqueness of a solution involves the use of nonlinear functional analysis techniques. In this talk, we will use a class of finite element methods called embedded discontinuous Galerkin (EDG) for the PFC equation. We will show that the scheme is unconditionally energy stable and uniquely solvable.