A Convergent evolving finite element algorithm for Willmore flow of closed surfaces

DOI10.1007/s00211-021-01238-zzbMath1496.65165arXiv2007.15257OpenAlexW3211845957MaRDI QIDQ2068350

Balázs Kovács, Buyang Li, Christian Lubich

Publication date: 19 January 2022

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.15257

zbMATH Keywords

finite element algorithmWillmore flowsurface diffusion flow

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) 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) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) PDEs on manifolds (35R01)

Related Items (14)

A Symmetrized Parametric Finite Element Method for Anisotropic Surface Diffusion of Closed Curves ⋮ Volume-preserving parametric finite element methods for axisymmetric geometric evolution equations ⋮ Stability and error estimates for non-linear Cahn-Hilliard-type equations on evolving surfaces ⋮ Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces ⋮ Evolving finite element methods with an artificial tangential velocity for mean curvature flow and Willmore flow ⋮ Convergence of a scheme for an elastic flow with tangential mesh movement ⋮ A Convexity-Preserving and Perimeter-Decreasing Parametric Finite Element Method for the Area-Preserving Curve Shortening Flow ⋮ A convergent finite element algorithm for mean curvature flow in arbitrary codimension ⋮ A structure‐preserving finite element approximation of surface diffusion for curve networks and surface clusters ⋮ Parametric finite element approximations for anisotropic surface diffusion with axisymmetric geometry ⋮ Numerical Surgery for Mean Curvature Flow of Surfaces ⋮ Numerical shape optimization of the Canham-Helfrich-Evans bending energy ⋮ New Artificial Tangential Motions for Parametric Finite Element Approximation of Surface Evolution ⋮ Unnamed Item

Uses Software

• DistMesh

Cites Work

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