标题： 能量稳定的混合有限元方法用于Rosensweig铁磁流体流动模型 显示英文标题

标题： Energy-stable mixed finite element methods for the Rosensweig ferrofluid flow model

摘要： 在本文中，我们考虑了Rosensweig铁磁流体流动模型的混合有限元半/全离散化方法。 我们首先在几个基本假设下建立了该模型的一些正则性结果。 然后我们证明了弱解的能量稳定性在半离散和全离散有限元解中被精确保持。 此外，我们证明了离散解的存在性和唯一性。 我们还导出了离散格式的最优误差估计。 最后，我们提供了数值实验来验证理论结果。 显示英文摘要

摘要： In this paper, we consider mixed finite element semi-/full discretizations of the Rosensweig ferrofluid flow model. We first establish some regularity results for the model under several basic assumptions. Then we show that the energy stability of the weak solutions is preserved exactly for both the semi-discrete and fully discrete finite element solutions. Moreover, we prove the existence and uniqueness of the discrete solutions. We also derive optimal error estimates for the discrete schemes. Finally, we provide numerical experiments to verify the theoretical results.