用于电荷载体传输和电渗模型的能量稳定离散化方法

Energetic Stable Discretization for Non-Isothermal Electrokinetics Model

We propose an edge averaged finite element(EAFE) discretization to solve the Heat-PNP (Poisson-Nernst-Planck) equations approximately. Our method enforces positivity of the computed charged density functions and temperature function. Also the thermodynamic consistent discrete energy estimate which resembles the thermodynamic second law of the Heat-PNP system is prescribed. Numerical examples are provided.

连续体中的嵌入结构：线性模型与有限元离散化

Embedding structures in continua: linear models and finite element discretizations

本文提出一个通用框架，用于将刚体、梁、壳等嵌入结构构件与连续体在能量意义上耦合，并证明问题及有限元近似适定，通过数值示例展示其通用性和稳健性。

Thermodynamically consistent and positivity-preserving discretization of the thin-film equation with thermal noise

In micro-fluidics not only does capillarity dominate but also thermal fluctuations become important. On the level of the lubrication approximation, this leads to a quasi-linear fourth-order parabolic equation for the film height $h$ driven by space-time white noise. The gradient flow structure of its deterministic counterpart, the thin-film equation, which encodes the balance between driving capillary and limiting viscous forces, provides the guidance for the thermodynamically consistent introduction of fluctuations. We follow this route on the level of a spatial discretization of the gradient…

保结构的MHD-漂移动理学离散化用于波-粒子相互作用

Structure-Preserving MHD-Driftkinetic Discretization for Wave-Particle Interactions

本文提出一种保结构的MHD-漂移动理学离散化方法，基于变分原理和FEEC-PIC框架，通过离散梯度时间积分器处理非二次磁矩能量项，实现能量守恒并成功模拟高能粒子激发的环向阿尔芬本征模。

保持结构的变分多尺度稳定化不可压缩纳维-斯托克斯方程

Structure-preserving Variational Multiscale Stabilization of the Incompressible Navier-Stokes Equations

本文提出了一种基于FEEC框架的变分多尺度稳定化方法，用于不可压缩纳维-斯托克斯方程，实现了结构保持的稳定化和高效并行计算。

超导伦敦方程的数值方法

Numerical approach to the London Equation of superconductivity

本研究提出一种求解三维空间II型超导体伦敦方程的FEM-BEM耦合离散化策略，经收敛性测试验证后，应用于等通量问题发现细长椭球存在非唯一最大化器的退化旋转方向。