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

TL;DR

This paper develops energy-stable mixed finite element methods for the Rosensweig ferrofluid flow model, ensuring stability, existence, uniqueness, and optimal error estimates, supported by numerical validation.

Contribution

It introduces energy-stable mixed finite element discretizations for the ferrofluid model, with proven stability, existence, uniqueness, and optimal error bounds.

Findings

Energy stability preserved in discretizations

Existence and uniqueness of discrete solutions proven

Optimal error estimates derived and verified numerically

Abstract

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.