A convergent and precise finite element scheme for Landau-Lifschitz-Gilbert equation

TL;DR

This paper presents a rigorously analyzed second-order finite element scheme for the Landau-Lifschitz-Gilbert equation, improving convergence proof and simplifying the iterative process.

Contribution

The authors introduce a modified scheme that ensures convergence and simplifies the inner iteration for solving the Landau-Lifschitz-Gilbert equation.

Findings

Proved convergence of the modified scheme.

Achieved second-order accuracy.

Simplified the iterative process.

Abstract

In this paper, we rigorously study an order 2 scheme that was previously proposed by some of the authors. A slight modification is proposed that enables us to prove the convergence of the scheme while simplifying in the same time the inner iteration.