The Landau-Brazovskii model is a well-known Landau model for finding the complex phase structures in microphase-separating systems ranging from block copolymers to liquid crystals. It is critical to design efficient numerical schemes for the Landau-Brazovskii model with energy dissipation and mass conservation properties. Here, we propose a mass conservative and energy stable scheme by combining the spectral deferred correction (SDC) method with the convex splitting technique to solve the Landau-Brazovskii model efficiently. An adaptive correction strategy for the SDC method is implemented to reduce the cost time and preserve energy stability. Numerical experiments, including two- and three-dimensional periodic crystals in the Landau-Brazovskii model, are presented to show the efficiency of the proposed numerical method.

翻译：Landau-Brazovskii模型是寻找从嵌段共聚物到液晶等微相分离体系中复杂相结构的著名Landau模型。设计具有能量耗散和质量守恒特性的Landau-Brazovskii模型高效数值方案至关重要。本文通过将谱延迟校正（SDC）方法与凸分裂技术相结合，提出了一种质量守恒且能量稳定的方案，以高效求解Landau-Brazovskii模型。采用SDC方法的自适应校正策略来减少计算时间并保持能量稳定性。通过Landau-Brazovskii模型中二维和三维周期晶体的数值实验，展示了所提数值方法的有效性。