An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation
An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation
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DOI：
10.1137/080738143
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发表时间：
2009-04
期刊：
影响因子：
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通讯作者：
S. Wise;Cheng Wang;J. Lowengrub
中科院分区：
文献类型：
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作者：
S. Wise;Cheng Wang;J. Lowengrub
对于相场晶体方程，我们提出了一种无条件能量稳定的有限差分格式。该方法基于离散能量的凸分裂，是半隐式的。隐式时间水平上的方程是非线性的，但表示严格凸函数的梯度，因此无论时间步长如何，都是唯一可解的。我们给出了保证格式收敛的局部时间误差估计。虽然本文主要讨论相场晶体方程，但大多数理论结果也适用于相关的Swift-Hohenberg方程。
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.