Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii

Andreas Prohl; Reiner Schaetzle; Lubomir Banas

doi:10.1007/s00211-009-0282-y

Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii

Andreas Prohl, Reiner Schaetzle, Lubomir Banas

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We prove the existence of weak solutions to the harmonic map heat flow, and wave maps into spheres of nonconstant radii. Weak solutions are constructed as proper limits of iterates from a fully practical scheme based on lowest order conforming finite elements, where discrete Lagrange multipliers are employed to exactly meet the sphere constraint at mesh-points. Computational studies are included to motivate interesting dynamics in two and three spatial dimensions. © 2010 Springer-Verlag.

Original language	English
Pages (from-to)	395-432
Number of pages	38
Journal	Numerische Mathematik
Volume	115
Issue number	3
DOIs	https://doi.org/10.1007/s00211-009-0282-y
Publication status	Published - May 2010

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AB - We prove the existence of weak solutions to the harmonic map heat flow, and wave maps into spheres of nonconstant radii. Weak solutions are constructed as proper limits of iterates from a fully practical scheme based on lowest order conforming finite elements, where discrete Lagrange multipliers are employed to exactly meet the sphere constraint at mesh-points. Computational studies are included to motivate interesting dynamics in two and three spatial dimensions. © 2010 Springer-Verlag.

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DO - 10.1007/s00211-009-0282-y

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JO - Numerische Mathematik

JF - Numerische Mathematik

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