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保持结构不变的非等温Cahn-Hilliard-Navier-Stokes系统逼近方法，该方法采用空间一致有限元离散与基于凸-凹分裂的隐式时间离散格式。首先将原系统重新表述为揭示方程结构的变分形式，随后将该形式用于后续的逼近过程。