Doubly Degenerate Diffuse Interface Models of Anisotropic Surface Diffusion

Doubly Degenerate Diffuse Interface Models of Surface Diffusion

We discuss two doubly degenerate Cahn-Hilliard (DDCH) models for isotropic surface diffusion. Degeneracy is introduced in both the mobility function and a restriction function associated to the chemical potential. Our computational results suggest that the restriction functions yield more accurate approximations of surface diffusion. We consider a slight generalization of a model that has appeared before, which is non-variational, meaning there is no clear energy that is dissipated along the solution trajectories. We also introduce a new variational and, more precisely, energy dissipative mode…

双非线性退化双曲-抛物型方程的离散对偶有限体积格式

Discrete duality finite volume schemes for doubly nonlinear degenerate hyperbolic-parabolic equations

针对双非线性退化双曲-抛物型方程，提出离散对偶有限体积格式，通过离散对偶公式和熵耗散不等式证明格式收敛到熵解。

非线性双重退化扩散方程的鲁棒、快速和自适应分裂格式

Robust, fast, and adaptive splitting schemes for nonlinear doubly-degenerate diffusion equations

针对非线性双重退化扩散方程，提出基于隐式Euler的分裂策略及多种迭代线性化格式，证明了L-scheme与改进L-scheme的收敛性，并开发基于后验估计的自适应M-scheme加速收敛，数值实验表明其比Newton格式更稳定高效。

双退化抛物方程的线性迭代方案

Linear iterative schemes for doubly degenerate parabolic equations

本文研究了双退化抛物方程的数值解法，提出了一种结合后向欧拉方法和混合有限元方法的稳定且局部守恒的方案，并开发了一种基于L方案的线性迭代方法，无需正则化，证明了其收敛性，并通过数值实验验证了理论结果。

一种用于双重退化抛物问题的自适应时空离散线性迭代格式

An adaptive, space-time discretized linear iterative scheme for doubly-degenerate parabolic problems

针对双重退化抛物问题，提出基于非线性项拆分的时空公式，用迭代线性化格式求解，证明其无条件收敛，分解非线性残差对偶范数得到后验估计，用于自适应时空求解器，数值实验表明该求解器能有效分配资源使误差快速衰减。

求解退化对流-扩散方程的紧致四阶双守恒主动通量方法，兼具最大原理保持限幅特性

A compact fourth-order doubly conservative active flux method with maximum-principle-preserving limiting for degenerate convection--diffusion equations

本文提出一种紧致四阶双守恒主动通量方法，用于求解退化对流-扩散方程，兼具最大原理保持限幅特性，数值实验验证了其四阶收敛性、界值保持性及对激波的精确分辨能力。