arXiv subjects

Nam Anh Nguyen

Publications and source records attributed to Nam Anh Nguyen.

3 recordsLinked to original sources

arXiv2026

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

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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arXiv2026

Error analysis for a Finite Element Discretization of a corotational harmonic map heat flow problem

We consider the harmonic map heat flow problem for a corotational case. For discretization of this problem we apply a $H^1$-conforming finite element method in space combined with a semi-implicit Euler time stepping. The semi-implicit Euler method results in a linear problem in each time step. We restrict to the regime of smooth solutions of the continuous problem and present an error analysis of this discretization method. This results in optimal order discretization error bounds. Key ingredients of the analysis are a discrete energy estimate, that mimics the energy dissipation of the continuous solution, and a convexity property that is essential for discrete stability and for control of the linearization error. We also present numerical results that validate the theoretical ones.

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arXiv2025

Discretization error analysis for a radially symmetric harmonic map heat flow problem

In this paper we study the harmonic map heat flow problem for a radially symmetric case. The corresponding partial dfferential equation plays a key role in many analyses of harmonic map heat flow problems. We consider a basic discretization method for this problem, namely a second order finite difference discretization in space combined with a semi-implicit Euler method in time. The semi-implicit Euler method results in a linear problem in each time step. We restrict to the regime of smooth solutions of the continuous problem and present an error analysis of this discretization method. This results in optimal order discretization error bounds (apart from a logarithmic term). We also present discrete energy estimates that mimic the decrease of the energy of the continuous solution.

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