Stability of a simple scheme for the approximation of elastic knots and self-avoiding inextensible curves

DOI10.1090/mcom/3633zbMath1476.65161arXiv1804.02206OpenAlexW3128667589MaRDI QIDQ4992222

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Publication date: 7 June 2021

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.02206

zbMATH Keywords

stabilitycurvesknot energybending energyelastic knotsself-avoidancetangent-point energies

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Nonlinear elasticity (74B20) Energy minimization in equilibrium problems in solid mechanics (74G65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Finite difference methods for boundary value problems involving PDEs (65N06) Curves in Euclidean and related spaces (53A04)

Related Items (10)

Knots with equal bridge index and braid index ⋮ Simulating Self-Avoiding Isometric Plate Bending ⋮ Surface penalization of self-interpenetration in linear and nonlinear elasticity ⋮ Tangent-point energies and ropelength as gamma-limits of discrete tangent-point energies on biarc curves ⋮ A descent scheme for thick elastic curves with self-contact and container constraints ⋮ Li-Yau type inequality for curves in any codimension ⋮ A speed preserving Hilbert gradient flow for generalized integral Menger curvature ⋮ Symmetric elastic knots ⋮ Sobolev gradients for the Möbius energy ⋮ Computing confined elasticae

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