Quadratic constraint consistency in the projection-free approximation of harmonic maps and bending isometries

Akrivis, Georgios; Bartels, Sören; Palus, Christian

doi:10.1090/mcom/4035

Quadratic constraint consistency in the projection-free approximation of harmonic maps and bending isometries
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by Georgios Akrivis, Sören Bartels and Christian Palus;

Math. Comp. 94 (2025), 2251-2269

DOI: https://doi.org/10.1090/mcom/4035

Published electronically: November 8, 2024

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Abstract:

We devise a projection-free iterative scheme for the approximation of harmonic maps that provides a second-order accuracy of the constraint violation and is unconditionally energy stable. A corresponding error estimate is valid under a mild but necessary discrete regularity condition. The method is based on the application of a BDF2 scheme and the considered problem serves as a model for partial differential equations with holonomic constraint. The performance of the method is illustrated via the computation of stationary harmonic maps and bending isometries.

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Quadratic constraint consistency in the projection-free approximation of harmonic maps and bending isometries
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Abstract: