Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

Convergent discretization of heat and wave map flows to spheres using approximate discrete Lagrange multipliers

Author(s): Sören Bartels; Christian Lubich; Andreas Prohl.
Journal: Math. Comp. 78 (2009), 1269-1292.
MSC (2000): Primary 65M12, 65M60, 35K55, 35Q35
Posted: February 18, 2009
MathSciNet review: 2501050
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We propose fully discrete schemes to approximate the harmonic map heat flow and wave maps into spheres. The finite-element based schemes preserve a unit length constraint at the nodes by means of approximate discrete Lagrange multipliers, satisfy a discrete energy law, and iterates are shown to converge to weak solutions of the continuous problem. Comparative computational studies are included to motivate finite-time blow-up behavior in both cases.

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