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

Bartels, Sören; Lubich, Christian; Prohl, Andreas

doi:10.1090/S0025-5718-09-02221-2

Convergent discretization of heat and wave map flows to spheres using approximate discrete Lagrange multipliers
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by Sören Bartels, Christian Lubich and Andreas Prohl;

Math. Comp. 78 (2009), 1269-1292

DOI: https://doi.org/10.1090/S0025-5718-09-02221-2

Published electronically: February 18, 2009

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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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