This analysis compares three finite element methods for harmonic map heat flow, highlighting convergence rates and computational efficiency.
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 R² to the unit sphere in R³ 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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Nguyen et al. (2025) studied this question.
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