标题： 基于Onsager变分原理的多孔介质方程移动网格方法 显示英文标题

标题： A Moving Mesh Method for Porous Medium Equation by the Onsager Variational Principle

摘要： 在本文中，我们介绍了一种新的方法，使用移动网格有限元方法来求解多孔介质方程，该方法利用Onsager变分原理作为近似工具。 连续问题和离散问题都是基于Onsager原理进行公式化的。 在半离散和全隐式离散方案中保持了能量耗散结构。 我们还开发了一个完全解耦的显式方案，使得在每个时间步中只需依次求解少量线性方程。 当初始网格被适当选择以确保初始数据的准确逼近时，数值方案表现出最优收敛率。 此外，该方法自然捕捉到了等待时间现象，而无需任何人工干预。 显示英文摘要

摘要： In this paper, we introduce a new approach to solving the porous medium equation using a moving mesh finite element method that leverages the Onsager variational principle as an approximation tool. Both the continuous and discrete problems are formulated based on the Onsager principle. The energy dissipation structure is maintained in the semi-discrete and fully implicit discrete schemes. We also develop a fully decoupled explicit scheme by which only a few linear equations are solved sequentially in each time step. The numerical schemes exhibit an optimal convergence rate when the initial mesh is appropriately selected to ensure accurate approximation of the initial data. Furthermore, the method naturally captures the waiting time phenomena without requiring any manual intervention.