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 journalArticle

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 languageEnglish
Pages (from-to)395-432
Number of pages38
JournalNumerische Mathematik
Volume115
Issue number3
DOIs
Publication statusPublished - May 2010

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Harmonic Maps
Heat Flow
Finite Element Approximation
Radius
Existence of Weak Solutions
Lagrange multipliers
Iterate
Weak Solution
Lowest
Mesh
Finite Element

Cite this

Prohl, Andreas ; Schaetzle, Reiner ; Banas, Lubomir. / Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii. In: Numerische Mathematik. 2010 ; Vol. 115, No. 3. pp. 395-432.
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Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii. / Prohl, Andreas; Schaetzle, Reiner; Banas, Lubomir.

In: Numerische Mathematik, Vol. 115, No. 3, 05.2010, p. 395-432.

Research output: Contribution to journalArticle

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