Error Estimates of Finite Element Method for the Incompressible Ferrohydrodynamics Equations

doi:10.1007/s42967-023-00347-w

Abstract

Abstract: In this paper, we consider the Shliomis ferrofluid model and study its numerical approximation. We investigate a first-order energy-stable fully discrete finite element scheme for solving the simplified ferrohydrodynamics (SFHD) equations. First, we establish the wellposedness and some regularity results for the solution of the SFHD model. Next we study the Euler semi-implicit time-discrete scheme for the SFHD systems and derive the L²-H¹ error estimates for the time-discrete solution. Moreover, certain regularity results for the time-discrete solution are proved rigorously. With the help of these regularity results, we prove the unconditional L²-H¹ error estimates for the finite element solution of the SFHD model. Finally, some three-dimensional numerical examples are carried out to demonstrate both the accuracy and efficiency of the fully discrete finite element scheme.

Key words: Shliomis model, Ferrofluids, Euler semi-implicit scheme, Mixed finite element methods, Error estimates, Unconditional convergence

CLC Number:

Shipeng Mao, Jiaao Sun. Error Estimates of Finite Element Method for the Incompressible Ferrohydrodynamics Equations[J]. Communications on Applied Mathematics and Computation, 2025, 7(2): 485-535.

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