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

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.

• Content Type Journal Article
• DOI 10.1007/s00211-009-0282-y
• Authors
  
  
  • L’ubomír Baňas, Heriot-Watt University Department of Mathematics and the Maxwell Institute for Mathematical Sciences Edinburgh EH14 4AS UK
  • Andreas Prohl, Mathematisches Institut der Universität Tübingen Auf der Morgenstelle 10 72076 Tübingen Germany
  • Reiner Schätzle, Mathematisches Institut der Universität Tübingen Auf der Morgenstelle 10 72076 Tübingen Germany
  
  

• Journal Numerische Mathematik
• Online ISSN 0945-3245
• Print ISSN 0029-599X

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Original source : http://www.springerlink.com/content/22g15824q3016g...