论文标题
时间分数相位方程的数值耗散
Numerical Energy Dissipation for Time-Fractional Phase-Field Equations
论文作者
论文摘要
相位方程的数值整合是一项精致的任务，需要在溶液的离散水平固有特性（例如能量耗散和最大原理）中恢复。尽管已经建立了经典相位场模型的能量耗散理论，但时间分数相位模型的相应理论仍然不完整。在本文中，我们使用一阶稳定的半显微L1方案研究了某些非局限性能量。特别是，我们将建立一个离散的分数能量法和一个离散的加权能量法。将研究$（2-α）$ - 订购L1标量辅助变量方案的扩展。此外，我们证明了与具有不均匀时间步骤的L1方案保留的能量结合。进行了几个数值实验以验证我们的理论分析。
The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the solution such as energy dissipation and maximum principle. Although the theory of energy dissipation for classical phase field models is well established, the corresponding theory for time-fractional phase-field models is still incomplete. In this article, we study certain nonlocal-in-time energies using the first-order stabilized semi-implicit L1 scheme. In particular, we will establish a discrete fractional energy law and a discrete weighted energy law. The extension for a $(2-α)$-order L1 scalar auxiliary variable scheme will be investigated. Moreover, we demonstrate that the energy bound is preserved for the L1 schemes with nonuniform time steps. Several numerical experiments are carried to verify our theoretical analysis.
