ELASTIC FLOW WITH JUNCTIONS: VARIATIONAL APPROXIMATION AND APPLICATIONS TO NONLINEAR SPLINES

DOI10.1142/S0218202512500376zbMath1252.76038OpenAlexW2165222838WikidataQ117202580 ScholiaQ117202580MaRDI QIDQ4649857

Harald Garcke, John W. Barrett, Robert Nürnberg

Publication date: 15 November 2012

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202512500376

zbMATH Keywords

junctionsparametric finite elementstangential movementWillmore flownonlinear splineselastic flowcurve networks

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (14)

An elastic flow for nonlinear spline interpolations in ℝⁿ ⋮ Willmore flow of planar networks ⋮ Li-Yau type inequality for curves in any codimension ⋮ Some minimization problems for planar networks of elastic curves ⋮ Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves ⋮ Stable approximations for axisymmetric Willmore flow for closed and open surfaces ⋮ Elastic flow of networks: long-time existence result ⋮ Elastic flow of networks: short-time existence result ⋮ A survey of the elastic flow of curves and networks ⋮ Long time existence of solutions to an elastic flow of networks ⋮ Degenerate elastic networks ⋮ A Second Order Gradient Flow of p-Elastic Planar Networks ⋮ Gradient flow dynamics of two-phase biomembranes: Sharp interface variational formulation and finite element approximation ⋮ Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds

Uses Software

• SuiteSparseQR

Cites Work

• Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves
• A parametric finite element method for fourth order geometric evolution equations
• Proof of the double bubble conjecture
• Evolution of Elastic Curves in $\Rn$: Existence and Computation
• SNAPPING ELASTIC CURVES AS A ONE-DIMENSIONAL ANALOGUE OF TWO-COMPONENT LIPID BILAYERS
• Error analysis for the elastic flow of parametrized curves
• The approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistribute
• The influence of elasticity on analysis: The classic heritage
• Computation of geometric partial differential equations and mean curvature flow
• On the Variational Approximation of Combined Second and Fourth Order Geometric Evolution Equations
• Equilibria of the Curvature Functional and Manifolds of Nonlinear Interpolating Spline Curves
• Interpolations with elasticae in Euclidean spaces
• Numerical approximation of gradient flows for closed curves in Rd
• Parametric Approximation of Willmore Flow and Related Geometric Evolution Equations

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