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.

中文翻译：

---

Mullins-Sekerka问题的结构保持前向跟踪有限元方法

我们介绍并分析了一个数学模型的完全离散近似，该数学模型用于比热可忽略不计的材料的凝固和液化。该模型是一个双边 Mullins-Sekerka 问题。离散化使用空间中的有限元和移动自由边界的独立参数化。我们证明了引入方案的无条件稳定性和精确体积守恒。几个数值模拟，包括近结晶表面能，证明了所提出的数值方法的实用性和准确性。