An Energy Stable and Convergent Finite-Difference Scheme for the Modified Phase Field Crystal Equation

Authors:
C. Wang;S. M. Wise
Affiliations:
cwang1@umassd.edu;swise@math.utk.edu
Venue:
SIAM Journal on Numerical Analysis
Year:
2011

Citing 5
Cited 3

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An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation

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An adaptive time-stepping strategy for solving the phase field crystal model

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Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation

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Abstract

We present an unconditionally energy stable finite difference scheme for the Modified Phase Field Crystal equation, a generalized damped wave equation for which the usual Phase Field Crystal equation is a special degenerate case. The method is based on a convex splitting of a discrete pseudoenergy 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 a local-in-time error estimate that ensures the pointwise convergence of the scheme.