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 | |
| Publication status | Published - May 2010 |
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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 journal › Article
TY - JOUR
T1 - Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii
AU - Prohl, Andreas
AU - Schaetzle, Reiner
AU - Banas, Lubomir
PY - 2010/5
Y1 - 2010/5
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=77952094579&partnerID=8YFLogxK
U2 - 10.1007/s00211-009-0282-y
DO - 10.1007/s00211-009-0282-y
M3 - Article
VL - 115
SP - 395
EP - 432
JO - Numerische Mathematik
JF - Numerische Mathematik
SN - 0029-599X
IS - 3
ER -