A numerical method for coupled surface and grain boundary motion

DOI10.1017/S0956792508007390zbMath1141.74018arXivmath/0702503OpenAlexW1964707967MaRDI QIDQ3515473

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Publication date: 29 July 2008

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702503

zbMATH Keywords

surface diffusionfinite difference methodsbi-crystalquarter loop geometry

Mathematics Subject Classification ID

Crystalline structure (74E15) Finite difference methods applied to problems in solid mechanics (74S20)

Related Items (9)

A numerical framework for singular limits of a class of reaction diffusion problems ⋮ A structure‐preserving finite element approximation of surface diffusion for curve networks and surface clusters ⋮ Mean curvature flow by the Allen–Cahn equation ⋮ Grain boundary migration with thermal grooving effects: a numerical approach ⋮ Numerical simulation and linear well-posedness analysis for a class of three-phase boundary motion problems ⋮ Stability of travelling wave solutions for coupled surface and grain boundary motion ⋮ A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds: application to a model of cell migration and chemotaxis ⋮ The approximation of planar curve evolutions by stable fully implicit finite element schemes that equidistribute ⋮ Finite-element approximation of coupled surface and grain boundary motion with applications to thermal grooving and sintering

Cites Work

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• A finite element method for surface diffusion: the parametric case.
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• Efficient algorithms for diffusion-generated motion by mean curvature
• On three-phase boundary motion and the singular limit of a vector-valued Ginzburg-Landau equation
• Semi-implicit level set methods for curvature and surface diffusion motion
• A numerical method for tracking curve networks moving with curvature motion
• Evolution of Elastic Curves in $\Rn$: Existence and Computation
• Computation of geometric partial differential equations and mean curvature flow
• On the Variational Approximation of Combined Second and Fourth Order Geometric Evolution Equations

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