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A structure‐preserving finite element approximation of surface diffusion for curve networks and surface clusters

https://doi.org/10.1002/num.22921
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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A variational formulation of anisotropic geometric evolution equations in higher dimensions
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A convergent evolving finite element algorithm for Willmore flow of closed surfaces
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The effect of thermal grooving on grain boundary motion
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Stability, microstructural evolution, grain growth, and coarsening in a two-dimensional two-phase microstructure
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Parametric finite element approximations of curvature-driven interface evolutions
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Numerical simulations of immiscible fluid clusters
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A finite element method for surface diffusion: the parametric case
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A parametric finite element method for solid-state dewetting problems with anisotropic surface energies
inferredcites →https://doi.org/10.1016/j.jcp.2021.110531openalex-snapshot
A perimeter-decreasing and area-conserving algorithm for surface diffusion flow of curves
inferredcites →https://doi.org/10.1016/j.jcp.2021.110658openalex-snapshot
An energy-stable parametric finite element method for anisotropic surface diffusion
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Non-linear stability of double bubbles under surface diffusion
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Electromigration of intergranular voids in metal films for microelectronic interconnects
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Handbook of Numerical Analysis
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A numerical method for coupled surface and grain boundary motion
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Finite-element approximation of coupled surface and grain boundary motion with applications to thermal grooving and sintering
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Computation of geometric partial differential equations and mean curvature flow
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A Variational Approach to Crystalline Triple-Junction Motion
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ANALYSIS OF FAILURE MECHANISMS IN THE INTERCONNECT LINES OF MICROELECTRONIC CIRCUITS
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Theory of Thermal Grooving
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The Surface Evolver
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Minimal perimeter for N identical bubbles in two dimensions: Calculations and simulations
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An energy-stable parametric finite element method for simulating solid-state dewetting
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Numerical approximation of anisotropic geometric evolution equations in the plane
inferredcites →https://doi.org/10.1098/rspa.2012.0392openalex-snapshot
Are large perimeter- minimizing two-dimensional clusters of equal-area bubbles hexagonal or circular?
inferredcites →https://doi.org/10.1103/physreve.69.031409openalex-snapshot
Three-dimensional bubble clusters: Shape, packing, and growth rate
inferredcites →https://doi.org/10.1103/physreve.78.011604openalex-snapshot
Phase-field model for multiphase systems with preserved volume fractions
inferredcites →https://doi.org/10.1103/physrevlett.93.208301openalex-snapshot
Structure of Random Foam
inferredcites →https://doi.org/10.1103/revmodphys.79.821openalex-snapshot
Colloquium: Soap bubble clusters
inferredcites →https://doi.org/10.1107/s0108767399012830openalex-snapshot
Double crystals
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On the Variational Approximation of Combined Second and Fourth Order Geometric Evolution Equations
inferredcites →https://doi.org/10.1137/19m1251345openalex-snapshot
Sharp-Interface Model for Simulating Solid-State Dewetting in Three Dimensions
inferredcites →https://doi.org/10.1137/19m1281666openalex-snapshot
A Parametric Finite Element Method for Solid-State Dewetting Problems in Three Dimensions
inferredcites →https://doi.org/10.1137/21m1406751openalex-snapshot
A Structure-Preserving Parametric Finite Element Method for Surface Diffusion
inferredcites →https://doi.org/10.1137/s0036141097320675openalex-snapshot
The Surface Diffusion Flow for Immersed Hypersurfaces
inferredcites →https://doi.org/10.1142/s0129167x9600044xopenalex-snapshot
OPEN PROBLEMS IN SOAP BUBBLE GEOMETRY
inferredcites →https://doi.org/10.1142/s0218202508003066openalex-snapshot
ALLEN–CAHN SYSTEMS WITH VOLUME CONSTRAINTS
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Algorithm 832
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Modelling sintering at different length scales
inferredcites →https://doi.org/10.14492/hokmj/1362406637openalex-snapshot
Linearized stability analysis of surface diffusion for hypersurfaces with triple lines
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On pinching of curves moved by surface diffusion
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Proof of the planar triple bubble conjecture
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On the Surface Diffusion Flow with Triple Junctions in Higher Space Dimensions
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A structure preserving front tracking finite element method for the Mullins–Sekerka problem
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The standard double soap bubble in R2uniquely minimizes perimeter
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The Structure of Singularities in Soap-Bubble-Like and Soap-Film-Like Minimal Surfaces
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Proof of the Double Bubble Conjecture
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Proof of the Double Bubble Conjecture
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Size and Shape Evolution of GaAsSb-Capped InAs/GaAs Quantum Dots: Dependence on the Sb Content
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A phase field model for the electromigration of intergranular voids
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Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies
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A projection method for motion of triple junctions by level sets
inferredcites →https://doi.org/10.4208/jcm.2205-m2021-0237openalex-snapshot
An Energy-Stable Parametric Finite Element Method for Simulating Solid-State Dewetting Problems in Three Dimensions
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Existence and uniqueness of standard bubble clusters of given volumes in $\mathbb{R}^N$
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Standard planar double bubbles are dynamically stable under surface diffusion flow
inferredcites →https://doi.org/10.48550/arxiv.1505.02979openalex-snapshot
Standard Planar Double Bubbles are Stable under Surface Diffusion Flow
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A singular limit for a system of degenerate Cahn-Hilliard equations

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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A Stabilized Parametric Finite Element Method for Surface Diffusion With an Arbitrary Surface Energy
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A structure-preserving parametric finite element method for geometric flows with anisotropic surface energy
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A structure-preserving finite element method for the multi-phase Mullins–Sekerka problem with triple junctions
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A Diffuse-Interface Approach for Solid-State Dewetting with Anisotropic Surface Energies
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A structure-preserving parametric finite element method with optimal energy stability condition for anisotropic surface diffusion
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Dynamics of small solid particles on substrates of arbitrary topography
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Structure-preserving discretizations of two-phase Navier–Stokes flow using fitted and unfitted approaches
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Predictor-corrector, BGN-based parametric finite element methods for surface diffusion
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A Symmetrized Parametric Finite Element Method for Anisotropic Surface Diffusion in Three Dimensions
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Structure-Preserving Parametric Finite Element Method for Surface Diffusion Based on Lagrange Multiplier Approaches
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A Parametric Finite Element Method for a Degenerate Multi-Phase Stefan Problem with Triple Junctions
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Dynamics of Small Solid Particles on Substrates of Arbitrary Topography
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Efficient Energy-Stable Parametric Finite Element Methods for Surface Diffusion Flow and Applications in Solid-State Dewetting
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