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，该方法在空间上采用协调有限元，在时间离散上采用基于凸-凹分裂的隐式格式。首先将系统重写为揭示方程结构的变分形式，该形式随后用于后续的逼近过程。