An energy-decreasing algorithm for the finite element approximation of ferronematic equilibrium states

TL;DR

This paper introduces an energy-decreasing finite element algorithm for modeling two-dimensional ferronematic equilibrium states, utilizing a decomposition-coordination framework and Uzawa-like iteration.

Contribution

It presents a novel energy-decreasing algorithm specifically designed for finite element approximation of ferronematic states with a new computational framework.

Findings

Algorithm effectively minimizes harmonic energy in simulations.

Numerical experiments demonstrate good computational performance.

Framework successfully handles nonlinear orientation constraints.

Abstract

We develop an energy-decreasing algorithm for the finite element approximation of two-dimensional ferronematic equilibrium states. The problem is formulated as the minimization of the harmonic energy of two two-dimensional vector fields, both with prescribed length, together with an additional nonlinear relation on the orientation of the two vectors. The finite element setting is based on piecewise continuous finite elements on a weakly acute triangulation. The computational realization of the energy-decreasing algorithm employs a decomposition-coordination framework and a Uzawa-like iteration. Numerical experiments are presented to illustrate the computational performances of the algorithm.