Stable approximations for axisymmetric Willmore flow for closed and open surfaces

DOI10.1051/m2an/2021014zbMath1500.65058arXiv1911.01132OpenAlexW3136159865WikidataQ114105438 ScholiaQ114105438MaRDI QIDQ5154004

John W. Barrett, Robert Nürnberg, Harald Garcke

Publication date: 1 October 2021

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.01132

zbMATH Keywords

stabilityclamped boundary conditionsparametric finite elementstangential movementNavier boundary conditionsaxisymmetryWillmore flowspontaneous curvatureline energyGaussian curvature energyHelfrich flowADE model

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Biomechanics (92C10) Membranes (74K15) Biomechanical solid mechanics (74L15) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Axially symmetric solutions to PDEs (35B07) Flows related to mean curvature (53E10)

Related Items (5)

Volume-preserving parametric finite element methods for axisymmetric geometric evolution equations ⋮ Parametric finite element approximations for anisotropic surface diffusion with axisymmetric geometry ⋮ On the convergence of the Willmore flow with Dirichlet boundary conditions ⋮ Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds ⋮ Stable Discretizations of Elastic Flow in Riemannian Manifolds

Uses Software

• UMFPACK

Cites Work

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• Error analysis for the approximation of axisymmetric Willmore flow by \(C^{1}\)-finite elements
• Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves
• A parametric finite element method for fourth order geometric evolution equations
• Modelling and simulations of multi-component lipid membranes and open membranes via diffuse interface approaches
• Computational parametric Willmore flow
• A numerical scheme for axisymmetric solutions of curvature-driven free boundary problems, with applications to the Willmore flow
• Variational discretization of axisymmetric curvature flows
• Finite element methods for fourth order axisymmetric geometric evolution equations
• A finite element method for surface restoration with smooth boundary conditions
• Min-max theory and the Willmore conjecture
• An algorithm for the elastic flow of surfaces
• Computational Parametric Willmore Flow with Spontaneous Curvature and Area Difference Elasticity Effects
• Error analysis for the elastic flow of parametrized curves
• Boundary value problems for variational integrals involving surface curvatures
• Parametric finite element approximations of curvature-driven interface evolutions
• Stresses in lipid membranes
• ELASTIC FLOW WITH JUNCTIONS: VARIATIONAL APPROXIMATION AND APPLICATIONS TO NONLINEAR SPLINES
• Stable variational approximations of boundary value problems for Willmore flow with Gaussian curvature
• Parametric Approximation of Willmore Flow and Related Geometric Evolution Equations
• Stable Discretizations of Elastic Flow in Riemannian Manifolds
• The effect of spontaneous curvature on a two-phase vesicle
• Algorithm 832
• Numerical approximation of curve evolutions in Riemannian manifolds

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