Numerical Analysis for a System Coupling Curve Evolution to Reaction Diffusion on the Curve

DOI10.1137/16M1083682zbMath1365.65218arXiv1607.01726OpenAlexW2963116825WikidataQ117202070 ScholiaQ117202070MaRDI QIDQ5347532

John W. Barrett, Vanessa Styles, Klaus Deckelnick

Publication date: 24 May 2017

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

Full work available at URL: https://arxiv.org/abs/1607.01726

zbMATH Keywords

error analysisparametric finite elementssurface PDEtangential motiondiffusion induced grain boundary motionforced curve shortening flow

Mathematics Subject Classification ID

Related Items (19)

Finite element error analysis for a system coupling surface evolution to diffusion on the surface ⋮ Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces ⋮ Finite Element Approximation of Level Set Motion by Powers of the Mean Curvature ⋮ Linearly implicit full discretization of surface evolution ⋮ Convergence of finite elements on an evolving surface driven by diffusion on the surface ⋮ A Convexity-Preserving and Perimeter-Decreasing Parametric Finite Element Method for the Area-Preserving Curve Shortening Flow ⋮ Numerical analysis for a system coupling curve evolution attached orthogonally to a fixed boundary, to a reaction–diffusion equation on the curve ⋮ A symmetrized parametric finite element method for simulating solid-state dewetting problems ⋮ Short time existence for coupling of scaled mean curvature flow and diffusion ⋮ Qualitative properties for a system coupling scaled mean curvature flow and diffusion ⋮ Convergence of Dziuk's Linearly Implicit Parametric Finite Element Method for Curve Shortening Flow ⋮ A convergent algorithm for forced mean curvature flow driven by diffusion on the surface ⋮ Mini-workshop: PDE models of motility and invasion in active biosystems. Abstracts from the mini-workshop held October 22--28, 2017 ⋮ Unnamed Item ⋮ Convergence of Dziuk's Fully Discrete Linearly Implicit Scheme for Curve Shortening Flow ⋮ Finite Element Approximation of a System Coupling Curve Evolution with Prescribed Normal Contact to a Fixed Boundary to Reaction-Diffusion on the Curve ⋮ Tracking the critical points of curves evolving under planar curvature flows ⋮ 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

Cites Work

• Unnamed Item
• Curve shortening flow coupled to lateral diffusion
• A parametric finite element method for fourth order geometric evolution equations
• Classical solutions for diffusion-induced grain-boundary motion
• Computations of bidirectional grain boundary dynamics in thin metallic films
• Bi-directional diffusion induced grain boundary motion with triple junctions
• An ALE ESFEM for solving PDEs on evolving surfaces
• The approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistribute
• Finite elements on evolving surfaces
• Finite element error bounds for a curve shrinking with prescribed normal contact to a fixed boundary
• 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

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