论文标题
标量辅助变量（SAV）方案的错误估算到Cahn-Hilliard方程
Error estimates for the scalar auxiliary variable (SAV) scheme to the Cahn-Hilliard equation
论文作者
论文摘要
最佳误差估计仅取决于$ \ varepsilon^{ - 1} $的多项式程度，这是为Cahn-Hilliard方程的时间半混凝土方案而建立的，该方程基于标量辅助变量（SAV）表格。我们分析的关键是将SAV时间步长方案的结构转换回与Cahn-Hilliard方程的原始格式兼容的形式，这使得使用光谱估计值来处理非线性术语。基于SAV数值方案的转换，时间半半混凝土方案的最佳误差估计仅取决于$ \ varepsilon^{ - 1} $而不是指数级的低多项式顺序，而不是使用数学诱导，光谱论证，频谱参数，以及某些非属性属性的超级范围。提供了数值示例来说明离散的能量衰减特性并验证我们的理论收敛分析。
The optimal error estimate that depending only on the polynomial degree of $ \varepsilon^{-1}$ is established for the temporal semi-discrete scheme of the Cahn-Hilliard equation, which is based on the scalar auxiliary variable (SAV) formulation. The key to our analysis is to convert the structure of the SAV time-stepping scheme back to a form compatible with the original format of the Cahn-Hilliard equation, which makes it feasible to use spectral estimates to handle the nonlinear term. Based on the transformation of the SAV numerical scheme, the optimal error estimate for the temporal semi-discrete scheme which depends only on the low polynomial order of $\varepsilon^{-1}$ instead of the exponential order, is derived by using mathematical induction, spectral arguments, and the superconvergence properties of some nonlinear terms. Numerical examples are provided to illustrate the discrete energy decay property and validate our theoretical convergence analysis.
