论文标题
部分可观测时空混沌系统的无模型预测
An unconditionally energy stable and positive upwind DG scheme for the Keller-Segel model
论文作者
论文摘要
由于它们固有的对流性质，凯勒 - 塞格方程的合理离散化已成为一个非常具有挑战性的问题。本文旨在为Keller-Segel模型引入一种新的前风，质量保守，积极和能量性的不连续的Galerkin方案。这种方法基于方程的梯度流结构。此外，我们根据离散化的上述特性显示了一些数值实验。获得的数值结果强调了在趋化性崩溃的情况下，在出现非常陡峭的梯度的情况下，近似值的真正良好行为。
The well-suited discretization of the Keller-Segel equations for chemotaxis has become a very challenging problem due to the convective nature inherent to them. This paper aims to introduce a new upwind, mass-conservative, positive and energy-dissipative discontinuous Galerkin scheme for the Keller-Segel model. This approach is based on the gradient-flow structure of the equations. In addition, we show some numerical experiments in accordance with the aforementioned properties of the discretization. The numerical results obtained emphasize the really good behaviour of the approximation in the case of chemotactic collapse, where very steep gradients appear.
