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

2023/09/30 by Georgios Akrivis, Akrivis, Georgios, Sören Bartels +3 · 4 citations
Engineering · Mathematics · Physics and Astronomy · #35J62 (35J50 35J57 65N30) #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2310.00381

openalex publication_date 2023/09/30 · openalex created_date 2023/10/04 · openalex updated_date 2026/07/28

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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• A comparative study of finite element methods for a class of harmonic map heat flow problems
• Error analysis for a Finite Element Discretization of a corotational harmonic map heat flow problem

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