微分和差分设置中变阶扩散方程的边值问题

从扩散角度理解微分方程

Understanding differential equations through diffusion point of view

提出一种基于D-迭代算法的新方法，通过将微分方程重新解释为扩散过程的极限，并预计算基本催化剂情况下的扩散过程，从而显著提高计算效率。

Stability analysis and error estimates of local discontinuous Galerkin method for convection-diffusion equations on overlapping mesh with non-periodic boundary conditions

A new local discontinuous Galerkin (LDG) method for convection-diffusion equations on overlapping meshes with periodic boundary conditions was introduced in \cite{Overlap1}. With the new method, the primary variable $u$ and the auxiliary variable $p=u_x$ are solved on different meshes. In this paper, we will extend the idea to convection-diffusion equations with non-periodic boundary conditions, i.e. Neumann and Dirichlet boundary conditions. The main difference is to adjust the boundary cells. Moreover, we study the stability and suboptimal error estimates. Finally, numerical experiments are …

具有Dirichlet边界条件的保极值原理非局部扩散模型

Maximum principle preserving nonlocal diffusion model with Dirichlet boundary condition

本文提出一类具有Dirichlet边界条件且保持极值原理的非局部扩散模型，利用其变分结构证明适定性与收敛性，并通过设计权函数实现最优的二阶收敛。

分数扩散方程的边界条件

Boundary Conditions for Fractional Diffusion

本文推导了分数扩散方程的物理意义边界条件，通过质量平衡方法分析，并讨论了吸收和反射边界条件的理论性质与数值解。

微分形式的对流扩散问题的欧拉和半拉格朗日方法

Eulerian and Semi-Lagrangian Methods for Convection-Diffusion for Differential Forms

针对有界域上微分形式的广义线性瞬态对流扩散问题，基于离散微分形式的伽辽金近似，构造了新的欧拉和半拉格朗日方法用于李导数的离散化，并讨论了实现细节及其在运动介质中涡流方程离散化中的应用。

具有自扩散的偏微分方程非线性分裂算法

A Nonlinear Splitting Algorithm for Systems of Partial Differential Equations with self-Diffusion

本文提出一种非线性分裂算法，用于求解包含自扩散的偏微分方程组，通过建立通用模型并进行数值分析，验证了算法的稳定性和收敛性。