Finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii
Banas, Lubomir
Banas
Lubomir
Prohl, Andreas
Prohl
Andreas
Schätzle, Reiner
Schätzle
Reiner
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.
115
3
395-432
395-432
Springer
2010