3 citations · 3 across the 6 of their papers we have counts for
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Linear and entropy-stable scheme for the dynamic van der Waals model of non-isothermal liquid-vapor flows
Yunzhuo Guo, Zhonghua Qiao, Xianmin Xu
In this paper, we propose a linear and decoupled fully discrete scheme that preserves the entropy production property for the dynamic van der Waals model. This model provides a the…
The Onsager principle and structure preserving numerical schemes
Huangxin Chen, Hailiang Liu, Xianmin Xu
We present a natural framework for constructing energy-stable time discretization schemes. By leveraging the Onsager principle, we demonstrate its efficacy in formulating partial d…
A Variational Discretization Method for Mean Curvature Flows by the Onsager Principle
Yihe Liu, Xianmin Xu
The mean curvature flow describes the evolution of a surface (a curve) with normal velocity proportional to the local mean curvature. It has many applications in mathematics, scien…
A Moving Mesh Method for Porous Medium Equation by the Onsager Variational Principle
Si Xiao, Xianmin Xu
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 ap…