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arXiv · 2508.20590

A comparative study of finite element methods for a class of harmonic map heat flow problems

Nam Anh Nguyen·Arnold Reusken
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Abstract

In this paper, we review and systematically compare three finite element discretization methods for a harmonic map heat flow problem from the unit disk in $\mathbb{R}^2$ to the unit sphere in $\mathbb{R}^3$ in an unified framework. Numerical tests validate the convergence rates in a regime of smooth solutions and are used to compare the methods in terms of computational efficiency. For one of the methods a discrete inf-sup stability result is derived.

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Nam Anh Nguyen, Arnold Reusken. 2026-07-27. A comparative study of finite element methods for a class of harmonic map heat flow problems. https://arxiv.org/abs/2508.20590

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