Approximation of Cahn–Hilliard diffuse interface models using parallel adaptive mesh refinement and coarsening with C 1 elements

A variational formulation and C 1 finite element scheme with adaptive mesh refinement and coarsening are developed for phase‐separation processes described by the Cahn–Hilliard diffuse interface model of transport in a mixture or alloy. The adaptive scheme is guided by a Laplacian jump indicator based on the corresponding term arising from the weak formulation of the fourth‐order non‐linear problem, and is implemented in a parallel solution framework. It is then applied to resolve complex evolving interfacial solution behavior for 2D and 3D simulations of the classic spinodal decomposition problem from a random initial mixture and to other phase‐transformation applications of interest. Simulation results and adaptive performance are discussed. The scheme permits efficient, robust multiscale resolution and interface characterization. Copyright © 2008 John Wiley & Sons, Ltd.