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 ferrohydrodynami...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 well-posedness 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 L^(2)-H^(1)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 L^(2)-H^(1)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.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12271514,11871467,12161141017)the National Key Research and Development Program of China(2023YFC3705701).
文摘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 well-posedness 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 L^(2)-H^(1)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 L^(2)-H^(1)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.
