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

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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.

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Authors and Affiliations

  1. Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK

    L’ubomír Baňas

  2. Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany

    Andreas Prohl & Reiner Schätzle

Authors
  1. L’ubomír Baňas
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  2. Andreas Prohl
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  3. Reiner Schätzle
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Correspondence to Andreas Prohl.

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Baňas, L., Prohl, A. & Schätzle, R. Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii. Numer. Math. 115, 395–432 (2010). https://doi.org/10.1007/s00211-009-0282-y

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  • DOI: https://doi.org/10.1007/s00211-009-0282-y

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