On fully practical finite element approximations of degenerate Cahn-Hilliard systems

DOI10.1051/m2an:2001133zbMath0987.35071OpenAlexW2161508768MaRDI QIDQ2781503

Harald Garcke, James F. Blowey, John W. Barrett

Publication date: 20 March 2002

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=M2AN_2001__35_4_713_0

zbMATH Keywords

convergence analysisphase separationdegenerate mobility matrix

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Initial-boundary value problems for higher-order parabolic equations (35K35) Degenerate parabolic equations (35K65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Cone conditions and properties of Sobolev spaces
• Finite element approximation of a fourth order nonlinear degenerate parabolic equation
• Finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy
• Nonnegativity preserving convergent schemes for the thin film equation
• Anisotropy in multi-phase systems: A phase field approach
• Dynamics of fluctuations and spinodal decomposition in polymer blends
• A multi-phase Mullins–Sekerka system: matched asymptotic expansions and an implicit time discretisation for the geometric evolution problem
• Splitting Algorithms for the Sum of Two Nonlinear Operators
• The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part I: Mathematical analysis
• The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part II: Numerical analysis
• Systems of Cahn–Hilliard Equations
• Finite element approximation of a model for phase separation of a multi-component alloy with a concentration-dependent mobility matrix
• Thermodynamically driven incompressible fluid mixtures
• FINITE ELEMENT APPROXIMATION OF A MODEL FOR PHASE SEPARATION OF A MULTI-COMPONENT ALLOY WITH NONSMOOTH FREE ENERGY AND A CONCENTRATION DEPENDENT MOBILITY MATRIX
• Numerical analysis of a model for phase separation of a multi-component alloy
• An error bound for the finite element approximation of a model for phase separation of a multi-component alloy
• 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
• Analyse Numerique d’un Probleme de Stefan a Deux Phases Par une Methode d’Elements Finis
• Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix
• Three-phase boundary motion by surface diffusion: Stability of a mirror symmetric stationary solution
• An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy with a concentration dependent mobility matrix
• A singular limit for a system of degenerate Cahn-Hilliard equations