A convergent finite element algorithm for mean curvature flow in arbitrary codimension
DOI10.4171/ifb/493arXiv2107.10577OpenAlexW4386054635MaRDI QIDQ6060950
Publication date: 6 November 2023
Published in: Interfaces and Free Boundaries (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2107.10577
mean curvature flowerror estimateshigher codimensionbackward difference formulasevolving surface finite elements
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) Numerical analysis (65-XX) Flows related to mean curvature (53E10)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A new tangentially stabilized 3D curve evolution algorithm and its application in virtual colonoscopy
- Mean curvature flow of pinched submanifolds to spheres
- Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves
- An algorithm for evolutionary surfaces
- Flow by mean curvature of convex surfaces into spheres
- On the parametric finite element approximation of evolving hypersurfaces in \(\mathbb R^3\)
- Anisotropic mean curvature flow for two-dimensional surfaces in higher codimension: A numerical scheme
- Level set approach to mean curvature flow in arbitrary codimension
- Singularities of the curve shrinking flow for space curves
- Shortening space curves and flow through singularities
- Convergence of finite elements on an evolving surface driven by diffusion on the surface
- An ALE ESFEM for solving PDEs on evolving surfaces
- Formal asymptotic expansions for symmetric ancient ovals in mean curvature flow
- A Convergent evolving finite element algorithm for Willmore flow of closed surfaces
- A planarity estimate for pinched solutions of mean curvature flow
- Pinched ancient solutions to the high codimension mean curvature flow
- A convergent algorithm for forced mean curvature flow driven by diffusion on the surface
- A convergent evolving finite element algorithm for mean curvature flow of closed surfaces
- A semi-Lagrangian scheme for the curve shortening flow in codimension-2
- P2Q2Iso2D=2D isoparametric FEM in Matlab
- Backward difference time discretization of parabolic differential equations on evolving surfaces
- Mean Curvature Flow in Higher Codimension: Introduction and Survey
- Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations
- Computation of geometric partial differential equations and mean curvature flow
- Finite elements on evolving surfaces
- Lectures on mean curvature flows in higher codimensions
- Higher-Order Finite Element Methods and Pointwise Error Estimates for Elliptic Problems on Surfaces
- CONVERGENCE OF A SEMI-DISCRETE SCHEME FOR THE CURVE SHORTENING FLOW
- High-order evolving surface finite element method for parabolic problems on evolving surfaces
- Convergence of Dziuk's Semidiscrete Finite Element Method for Mean Curvature Flow of Closed Surfaces with High-order Finite Elements
- A convergent finite element algorithm for generalized mean curvature flows of closed surfaces
- The Energy Technique for the Six-Step BDF Method
- Solving Ordinary Differential Equations II
- Numerical approximation of gradient flows for closed curves in Rd
- Discrete Gradient Flows for General Curvature Energies
- Anisotropic curve shortening flow in higher codimension
- Finite element methods for surface PDEs