Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints

TL;DR

This paper provides an error estimate for a finite element discretization of the harmonic map heat flow into spheres, focusing on nodal constraints and elementary approximation techniques.

Contribution

It introduces a novel error analysis for a standard finite element scheme with nodal constraints for harmonic map heat flow.

Findings

Error bounds for the discretization are established.

The analysis relies on elementary approximation results.

The scheme effectively handles linearized unit-length constraints.

Abstract

An error estimate for a canonical discretization of the harmonic map heat flow into spheres is derived. The numerical scheme uses standard finite elements with a nodal treatment of linearized unit-length constraints. The analysis is based on elementary approximation results and only uses the discrete weak formulation.