ENERGY STABILITY AND CONVERGENCE OF SAV BLOCK-CENTERED FINITE DIFFERENCE METHOD FOR GRADIENT FLOWS
ENERGY STABILITY AND CONVERGENCE OF SAV BLOCK-CENTERED FINITE DIFFERENCE METHOD FOR GRADIENT FLOWS
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梯度流SAV块心有限差分法的能量稳定性和收敛性
DOI：
10.1090/mcom/3428
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发表时间：
2019-09-01
影响因子：
2
通讯作者：
Rui, Hongxing
中科院分区：
文献类型：
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作者：
Li, Xiaoli;Shen, Jie;Rui, Hongxing
本文构造并分析了梯度流标量辅助变量Crank-Nicolson格式（SAV/CN-BCFD）的块中心有限差分空间离散化方法，并严格证明了该格式在各种离散范数下在时间和空间上都是二阶的.当配备自适应时间策略时，SAV/CN-BCFD方案是准确的并且非常有效。对典型的Allen-Cahn和Cahn-Hilliard方程的数值实验验证了我们的理论结果，并显示了SAV/CN-BCFD格式的鲁棒性和准确性。
We present in this paper construction and analysis of a block-centered finite difference method for the spatial discretization of the scalar auxiliary variable Crank-Nicolson scheme (SAV/CN-BCFD) for gradient flows, and show rigorously that the scheme is second-order in both time and space in various discrete norms. When equipped with an adaptive time strategy, the SAV/CN-BCFD scheme is accurate and extremely efficient. Numerical experiments on typical Allen-Cahn and Cahn-Hilliard equations are presented to verify our theoretical results and to show the robustness and accuracy of the SAV/CN-BCFD scheme.