Convergence of a finite element method for non-parametric mean curvature flow

DOI10.1007/s002110050166zbMath0838.65103OpenAlexW1965110070MaRDI QIDQ1907133

Gerhard Dziuk, Klaus Deckelnick

Publication date: 3 June 1996

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

Full work available at URL: https://doi.org/10.1007/s002110050166

zbMATH Keywords

convergenceerror estimatesfinite element methodconvection-diffusion equationDirichlet problemsmean curvature flow equationparabolic minimal-surface equation

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (13)

Finite element error analysis for a system coupling surface evolution to diffusion on the surface ⋮ Finite Element Approximation of Level Set Motion by Powers of the Mean Curvature ⋮ Evolving finite element methods with an artificial tangential velocity for mean curvature flow and Willmore flow ⋮ A symmetrized parametric finite element method for simulating solid-state dewetting problems ⋮ Convergence of Dziuk's Linearly Implicit Parametric Finite Element Method for Curve Shortening Flow ⋮ Semilinear mixed problems on Hilbert complexes and their numerical approximation ⋮ Geometric variational crimes: Hilbert complexes, finite element exterior calculus, and problems on hypersurfaces ⋮ Unnamed Item ⋮ Structure preserving discretization of Allen-Cahn type problems modeling the motion of phase boundaries ⋮ Stability of flat interfaces during semidiscrete solidification ⋮ Analysis of Constants in Error Estimates for the Finite Element Approximation of Regularized Nonlinear Geometric Evolution Equations ⋮ Convergence of Dziuk's Semidiscrete Finite Element Method for Mean Curvature Flow of Closed Surfaces with High-order Finite Elements ⋮ A convergent evolving finite element algorithm for mean curvature flow of closed surfaces

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