2024/11/30 by Yongke Wu, Wu, Yongke, Xiaoping Xie +1
Engineering · #Characterization and Applications of Magnetic Nanoparticles #Lattice Boltzmann Simulation Studies #Fluid Dynamics and Turbulent Flows
paper · pdf · doi:10.48550/arxiv.2412.00360
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.