Discrete Gradient Flows for General Curvature Energies

DOI10.1137/18M122844XzbMath1434.65178OpenAlexW2903314822MaRDI QIDQ5230627

Robert Nürnberg, Willy Dörfler

Publication date: 28 August 2019

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/18m122844x

zbMATH Keywords

finite element approximationgradient flowequidistributionclamped boundary conditionsoptical fibercurvature energy

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Anisotropy in solid mechanics (74E10) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Global differential geometry (53C99)

Related Items (3)

A convergent finite element algorithm for mean curvature flow in arbitrary codimension ⋮ High-Order Fully Discrete Energy Diminishing Evolving Surface Finite Element Methods for a Class of Geometric Curvature Flows ⋮ Computing confined elasticae

Uses Software

• UMFPACK
• ALBERTA

Cites Work

• Unnamed Item
• Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves
• An algorithm for evolutionary surfaces
• Computational parametric Willmore flow
• Design of adaptive finite element software. The finite element toolbox ALBERTA. With CD-ROM
• The Willmore boundary problem
• Nonlinear dynamics and loop formation in Kirchhoff rods with implications to the mechanics of DNA and cables
• Boundary value problems for the one-dimensional Willmore equation
• Evolution of Elastic Curves in $\Rn$: Existence and Computation
• A simple scheme for the approximation of the elastic flow of inextensible curves
• Error analysis for the elastic flow of parametrized curves
• The approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistribute
• Stability and Symmetry in the Navier Problem for the One-Dimensional Willmore Equation
• Computation of geometric partial differential equations and mean curvature flow
• CONVERGENCE OF A SEMI-DISCRETE SCHEME FOR THE CURVE SHORTENING FLOW
• A simple scheme for the approximation of self-avoiding inextensible curves
• A gradient flow for open elastic curves with fixed length and clamped ends
• Interpolations with elasticae in Euclidean spaces
• Numerical approximation of gradient flows for closed curves in Rd
• Algorithm 832

This page was built for publication: Discrete Gradient Flows for General Curvature Energies