Finite element approximation of a phase field model for surface diffusion of voids in a stressed solid

DOI10.1090/S0025-5718-05-01802-8zbMath1078.74050OpenAlexW1992674433MaRDI QIDQ5713216

John W. Barrett, Harald Garcke, Robert Nürnberg

Publication date: 12 December 2005

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-05-01802-8

zbMATH Keywords

convergenceelasticitydegenerate Cahn-Hilliard equationnonlinear degenerate parabolic system

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Structured surfaces and interfaces, coexistent phases (74A50) Finite element methods applied to problems in solid mechanics (74S05) Degenerate parabolic equations (35K65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

Related Items

A fitted finite element method for the numerical approximation of void electro-stress migration, Finite element approximation of a phase field model arising in nanostructure patterning, Isogeometric analysis of the Cahn-Hilliard phase-field model, Interface motion by interface diffusion driven by bulk energy: justification of a diffusive interface model, Optimal control of time-discrete two-phase flow driven by a diffuse-interface model, Evolution free-boundary problem for a stationary system of the theory of elasticity, On a phase field model of Cahn-Hilliard type for tumour growth with mechanical effects, Energy law preserving \(C^0\) finite element schemes for phase field models in two-phase flow computations, Solving the regularized, strongly anisotropic Cahn-Hilliard equation by an adaptive nonlinear multigrid method, Energy Law Preserving Finite Element Scheme for the Cahn-Hilliard Equation with Dynamic Boundary Conditions^†, Solvability of a free-boundary problem for a heterogeneous elastic body, Approximation of Cahn-Hilliard diffuse interface models using parallel adaptive mesh refinement and coarsening withC¹elements, Optimal Control of Sliding Droplets Using the Contact Angle Distribution

Uses Software

• ALBERT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Singularités en élasticité. (Singularities in elasticity)
• Cone conditions and properties of Sobolev spaces
• Finite element approximation of a fourth order nonlinear degenerate parabolic equation
• Dynamic solid-solid transitions with phase characterized by an order parameter
• Finite element approximation of a sixth order nonlinear degenerate parabolic equation
• A finite element analysis of the motion and evolution of voids due to strain and electromigration induced surface diffusion
• Nonnegativity preserving convergent schemes for the thin film equation
• On a Cahn--Hilliard model for phase separation with elastic misfit
• Numerical approximation of the Cahn-Larché equation
• On fully practical finite element approximations of degenerate Cahn-Hilliard systems
• On the Green's Function for the Biharmonic Equation in an Infinite Wedge
• Some Optimal Error Estimates for Piecewise Linear Finite Element Approximations
• The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part I: Mathematical analysis
• The Surface Diffusion Flow for Immersed Hypersurfaces
• On Cahn—Hilliard systems with elasticity
• Finite Element Approximation of Surfactant Spreading on a Thin Film
• Finite Element Approximation of a Degenerate Allen--Cahn/Cahn--Hilliard System
• Finite Element Approximation of a Phase Field Model for Void Electromigration
• The Cahn–Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature
• On the convergence of entropy consistent schemes for lubrication type equations in multiple space dimensions
• On the Cahn–Hilliard Equation with Degenerate Mobility
• Finite Element Approximation of the Cahn--Hilliard Equation with Degenerate Mobility
• Positivity-Preserving Numerical Schemes for Lubrication-Type Equations
• The Cahn-Hilliard equation with elasticity -- finite element approximation and qualitative studies
• Fast semi-analytic computation of elastic edge singularities