Convergence of Dziuk's Semidiscrete Finite Element Method for Mean Curvature Flow of Closed Surfaces with High-order Finite Elements

DOI10.1137/20M136935XzbMath1479.65008arXiv2101.03703WikidataQ114074151 ScholiaQ114074151MaRDI QIDQ4994420

Buyang Li

Publication date: 18 June 2021

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.03703

zbMATH Keywords

convergencemean curvature flowfinite element methoderror estimateevolving surface

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Degenerate parabolic equations (35K65) 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 (9)

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 ⋮ 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 ⋮ Erratum: Convergence of Dziuk’s Semidiscrete Finite Element Method for Mean Curvature Flow of Closed Surfaces with High-Order Finite Elements ⋮ Numerical Surgery for Mean Curvature Flow of Surfaces ⋮ New Artificial Tangential Motions for Parametric Finite Element Approximation of Surface Evolution ⋮ Unnamed Item ⋮ Convergence of Dziuk's Fully Discrete Linearly Implicit Scheme for Curve Shortening Flow

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Scalar conservation laws on moving hypersurfaces
• Curve shortening flow coupled to lateral diffusion
• An algorithm for evolutionary surfaces
• On the parametric finite element approximation of evolving hypersurfaces in \(\mathbb R^3\)
• Regularity theory for mean curvature flow
• Error estimates for a semi-implicit fully discrete element scheme for the mean curvature flow of graphs
• Convergence of finite elements on an evolving surface driven by diffusion on the surface
• Convergence of a finite element method for non-parametric mean curvature flow
• A convergent evolving finite element algorithm for mean curvature flow of closed surfaces
• Computation of geometric partial differential equations and mean curvature flow
• Finite elements on evolving surfaces
• Higher-Order Finite Element Methods and Pointwise Error Estimates for Elliptic Problems on Surfaces
• Approximation of domains with Lipschitzian boundary
• Discrete Anisotropic Curve Shortening Flow
• CONVERGENCE OF A SEMI-DISCRETE SCHEME FOR THE CURVE SHORTENING FLOW
• High-order evolving surface finite element method for parabolic problems on evolving surfaces
• On approximations of the curve shortening flow and of the mean curvature flow based on the DeTurck trick
• $L^2$-estimates for the evolving surface finite element method
• Convergence of Dziuk's Linearly Implicit Parametric Finite Element Method for Curve Shortening Flow
• Numerical approximation of gradient flows for closed curves in Rd
• Anisotropic curve shortening flow in higher codimension
• Numerical Analysis for a System Coupling Curve Evolution to Reaction Diffusion on the Curve
• Finite element methods for surface PDEs

This page was built for publication: Convergence of Dziuk's Semidiscrete Finite Element Method for Mean Curvature Flow of Closed Surfaces with High-order Finite Elements