Convergence of Dziuk's Linearly Implicit Parametric Finite Element Method for Curve Shortening Flow

DOI10.1137/19M1305483zbMath1452.65240MaRDI QIDQ5123986

Buyang Li

Publication date: 17 September 2020

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

zbMATH Keywords

convergenceerror estimatecurve shortening flowparametric finite element methodlinearly implicit

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Degenerate parabolic equations (35K65) 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) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items (5)

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 ⋮ Unnamed Item ⋮ Convergence of Dziuk's Fully Discrete Linearly Implicit Scheme for Curve Shortening Flow ⋮ Convergence of Dziuk's Semidiscrete Finite Element Method for Mean Curvature Flow of Closed Surfaces with High-order Finite Elements

Cites Work

• Unnamed Item
• Unnamed Item
• An algorithm for evolutionary surfaces
• On the parametric finite element approximation of evolving hypersurfaces in \(\mathbb R^3\)
• Error estimates for a semi-implicit fully discrete element scheme for the mean curvature flow of graphs
• 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
• Discrete Anisotropic Curve Shortening Flow
• CONVERGENCE OF A SEMI-DISCRETE SCHEME FOR THE CURVE SHORTENING FLOW
• On approximations of the curve shortening flow and of the mean curvature flow based on the DeTurck trick
• 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

This page was built for publication: Convergence of Dziuk's Linearly Implicit Parametric Finite Element Method for Curve Shortening Flow