In this work we propose and analyse a structure-preserving approximation of the non-isothermal Cahn-Hilliard-Navier-Stokes system using conforming finite elements in space and implicit time discretisation with convex-concave splitting. The system is first reformulated into a variational form which reveal the structure of the equations, which is then used in the subsequent approximation.

翻译：本文提出并分析了一种非等温Cahn-Hilliard-Navier-Stokes系统的保结构逼近方法，该方法采用空间上的协调有限元与基于凸凹分裂的隐式时间离散格式。系统首先被重新表述为能够揭示方程结构的变分形式，该形式随后被用于后续的逼近分析中。