Energy-preserving Mixed finite element methods for a ferrofluid flow model

TL;DR

This paper introduces energy-preserving mixed finite element methods for a ferrofluid flow model, ensuring stability, existence, uniqueness, and optimal error estimates, validated by numerical experiments.

Contribution

It develops a novel class of finite element methods that exactly preserve energy stability for ferrofluid flow models, with rigorous proofs and numerical validation.

Findings

Energy stability is preserved exactly in the numerical schemes.

Existence and uniqueness of discrete solutions are proven.

Optimal error estimates are derived and confirmed by experiments.

Abstract

In this paper, we develop a class of mixed finite element methods for the ferrofluid flow model proposed by Shliomis [Soviet Physics JETP, 1972]. We show that the energy stability of the weak solutions to the model is preserved exactly for both the semi- and fully discrete finite element solutions. Furthermore, we prove the existence and uniqueness of the discrete solutions and derive optimal error estimates for both the the semi- and fully discrete schemes. Numerical experiments confirm the theoretical results.