A Convexity-Preserving and Perimeter-Decreasing Parametric Finite Element Method for the Area-Preserving Curve Shortening Flow
DOI10.1137/22m1514404zbMath1522.65174arXiv2208.01324OpenAlexW4386093571MaRDI QIDQ6046756
Unnamed Author, Chun-Mei Su, Unnamed Author
Publication date: 6 September 2023
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2208.01324
error estimateparametric finite element methodconvexity-preservingarea-preserving curve shortening flowperimeter-decreasing
Nonlinear parabolic equations (35K55) 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)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Curve shortening flow coupled to lateral diffusion
- An algorithm for evolutionary surfaces
- A parametric finite element method for fourth order geometric evolution equations
- On the parametric finite element approximation of evolving hypersurfaces in \(\mathbb R^3\)
- A simple scheme for volume-preserving motion by mean curvature
- Convergence of a crystalline approximation for an area-preserving motion.
- Variational discretization of axisymmetric curvature flows
- Area-preserving curve-shortening flows: From phase separation to image processing
- Linking anisotropic sharp and diffuse surface motion laws via gradient flows
- A Convergent evolving finite element algorithm for Willmore flow of closed surfaces
- A fully discrete curve-shortening polygonal evolution law for moving boundary problems
- Optimal control of volume-preserving mean curvature flow
- A perimeter-decreasing and area-conserving algorithm for surface diffusion flow of curves
- Volume-preserving parametric finite element methods for axisymmetric geometric evolution equations
- Evolving finite element methods with an artificial tangential velocity for mean curvature flow and Willmore flow
- A convergent evolving finite element algorithm for mean curvature flow of closed surfaces
- Algorithms for Area Preserving Flows
- Parametric finite element approximations of curvature-driven interface evolutions
- Computation of geometric partial differential equations and mean curvature flow
- Numerical approximation of anisotropic geometric evolution equations in the plane
- On the Variational Approximation of Combined Second and Fourth Order Geometric Evolution Equations
- Semidiscrete Geometric Flows of Polygons
- The volume preserving mean curvature flow.
- The volume preserving mean curvature flow near spheres
- Discrete Anisotropic Curve Shortening Flow
- CONVERGENCE OF A SEMI-DISCRETE SCHEME FOR THE CURVE SHORTENING FLOW
- Volume-Preserving Mean Curvature Flow as a Limit of a Nonlocal Ginzburg-Landau Equation
- A numerical scheme for moving boundary problems that are gradient flows for the area functional
- On approximations of the curve shortening flow and of the mean curvature flow based on the DeTurck trick
- Curvature-Driven Flows: A Variational Approach
- On the Coarsening Rates for Attachment-Limited Kinetics
- Extrinsic Geometric Flows
- Convergence of Dziuk's Semidiscrete Finite Element Method for Mean Curvature Flow of Closed Surfaces with High-order Finite Elements
- Convergence of Dziuk's Linearly Implicit Parametric Finite Element Method for Curve Shortening Flow
- A Structure-Preserving Parametric Finite Element Method for Surface Diffusion
- Convergence of Dziuk's Fully Discrete Linearly Implicit Scheme for Curve Shortening Flow
- Convex and Discrete Geometry
- Numerical Analysis for a System Coupling Curve Evolution to Reaction Diffusion on the Curve
- The Mathematical Theory of Finite Element Methods
- Computational and qualitative aspects of evolution of curves driven by curvature and external force