Fully Discrete Finite Element Approximation for Anisotropic Surface Diffusion of Graphs

DOI10.1137/S0036142903434874zbMath1094.65098MaRDI QIDQ5700309

Charles M. Elliott, Gerhard Dziuk, Klaus Deckelnick

Publication date: 28 October 2005

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

zbMATH Keywords

error estimatesnumerical examplesfinite elementsurface diffusionanisotropicgeometric motionfourth order parabolic equationsecond order operator splitting

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) 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

A Symmetrized Parametric Finite Element Method for Anisotropic Surface Diffusion of Closed Curves ⋮ A perimeter-decreasing and area-conserving algorithm for surface diffusion flow of curves ⋮ A tangent-plane marker-particle method for the computation of three-dimensional solid surfaces evolving by surface diffusion on a substrate ⋮ Evolving finite element methods with an artificial tangential velocity for mean curvature flow and Willmore flow ⋮ A parametric finite element method for fourth order geometric evolution equations ⋮ A discrete scheme for parametric anisotropic surface diffusion ⋮ A parametric finite element method for solid-state dewetting problems with anisotropic surface energies ⋮ Parametric finite element approximations for anisotropic surface diffusion with axisymmetric geometry ⋮ Optimal error estimates of the local discontinuous Galerkin method for surface diffusion of graphs on Cartesian meshes ⋮ A Posteriori Error Estimates for the Laplace--Beltrami Operator on Parametric $C^2$ Surfaces ⋮ A Structure-Preserving Parametric Finite Element Method for Surface Diffusion ⋮ A finite element method for surface diffusion: the parametric case. ⋮ Error estimates of finite volume element method for the pollution in groundwater flow ⋮ A Convergent evolving finite element algorithm for Willmore flow of closed surfaces

This page was built for publication: Fully Discrete Finite Element Approximation for Anisotropic Surface Diffusion of Graphs