Journal of Scientific Computing
SIAM Journal on Numerical Analysis
An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models
SIAM Journal on Scientific Computing
A gradient stable scheme for a phase field model for the moving contact line problem
Journal of Computational Physics
An adaptive multigrid algorithm for simulating solid tumor growth using mixture models
Mathematical and Computer Modelling: An International Journal
SIAM Journal on Numerical Analysis
An adaptive time-stepping strategy for solving the phase field crystal model
Journal of Computational Physics
Journal of Computational Physics
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We present an unconditionally energy stable finite-difference scheme for the phase field crystal equation. The method is based on a convex splitting of a discrete energy and is semi-implicit. The equation at the implicit time level is nonlinear but represents the gradient of a strictly convex function and is thus uniquely solvable, regardless of time step size. We present local-in-time error estimates that ensure the convergence of the scheme. While this paper is primarily concerned with the phase field crystal equation, most of the theoretical results hold for the related Swift-Hohenberg equation as well.