We introduce and analyse a fully discrete approximation for a mathematical model for the solidification and liquidation of materials of negligible specific heat. The model is a two-sided Mullins--Sekerka problem. The discretization uses finite elements in space and an independent parameterization of the moving free boundary. We prove unconditional stability and exact volume conservation for the introduced scheme. Several numerical simulations, including for nearly crystalline surface energies, demonstrate the practicality and accuracy of the presented numerical method.

翻译：我们引入并分析一个完全离散的近似值,用于对可忽略不计的具体热量的材料进行固化和清理的数学模型,该模型是一个双向的穆林斯-塞克尔卡问题,离散在空间中使用有限的元素,并在移动的自由边界上使用独立的参数。我们证明,对引入的系统来说,我们无条件的稳定性和准确的量的保存。一些数字模拟,包括对近晶状地表能量的模拟,显示了所提出的数字方法的实用性和准确性。