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Approximation of Fractional Harmonic Maps by Antil, Harbir; Bartels, Sören; Schikorra, Armin is a scholarly article available to read on EtoBox.

What is Approximation of Fractional Harmonic Maps about?

This paper addresses the approximation of fractional harmonic maps. Besides a unit-length constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness results for critical points of the fractional Dirichlet energy on unit-length vector fields. We devise and analyze numerical methods for the approximation of various partial differential equations related to fractional harmonic maps. The compactness results imply the convergence of numerical approximations. Numerical examples on spin chain dynamics and point defects are presented to demonstrate the effectiveness of the proposed methods.

Author

Antil, Harbir; Bartels, Sören; Schikorra, Armin

Published

2021

Language

EN