An Efficient and Convergent Finite Element Scheme for Cahn--Hilliard Equations with Dynamic Boundary Conditions
DOI10.1137/19M1280740zbMath1458.35345arXiv1908.04910OpenAlexW2968867992MaRDI QIDQ5147763
Publication date: 28 January 2021
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1908.04910
convergencefinite elementsvariational formulationnumerical simulationdynamic boundary conditionsCahn-Hilliard problem
PDEs in connection with fluid mechanics (35Q35) 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) Initial-boundary value problems for nonlinear higher-order PDEs (35G31) Liquid-liquid two component flows (76T06) Mathematical modeling or simulation for problems pertaining to fluid mechanics (76-10)
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- Linear functional analysis. An application-oriented introduction. Translated from the 6th German edition by Robert Nürnberg
- Two-phase flow with mass density contrast: stable schemes for a thermodynamic consistent and frame-indifferent diffuse-interface model
- Passing from bulk to bulk-surface evolution in the Allen-Cahn equation
- Hitchhiker's guide to the fractional Sobolev spaces
- Higher-order Cahn-Hilliard equations with dynamic boundary conditions
- A Cahn-Hilliard model in a domain with non-permeable walls
- The Cahn-Hilliard equation with logarithmic potentials
- Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
- A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow
- The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions
- On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions
- On the Cahn-Hilliard equation
- Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy
- The Cahn-Hilliard equation with dynamic boundary conditions.
- Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model
- On stable, dissipation reducing splitting schemes for two-phase flow of electrolyte solutions
- An energetic variational approach for the Cahn-Hilliard equation with dynamic boundary condition: model derivation and mathematical analysis
- Convergence to equilibrium for the Cahn-Hilliard equation with dynamic boundary conditions
- Bound-preserving flux limiting schemes for DG discretizations of conservation laws with applications to the Cahn-Hilliard equation
- On the Cahn-Hilliard equation with dynamic boundary conditions and a dominating boundary potential
- Time periodic solutions of Cahn-Hilliard systems with dynamic boundary conditions
- Cahn-Hilliard equation with dynamic boundary conditions and mass constraint on the boundary
- Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy
- On the stability of the $L^2$ projection in $H^1(\Omega)$
- On fully practical finite element approximations of degenerate Cahn-Hilliard systems
- Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich–Schwoebel Type Energy: Application to Thin Film Epitaxy
- The Dynamics of Nucleation for the Cahn–Hilliard Equation
- A Cahn–Hilliard model in bounded domains with permeable walls
- Convergence to steady states of solutions of the Cahn–Hilliard and Caginalp equations with dynamic boundary conditions
- Front migration in the nonlinear Cahn-Hilliard equation
- Direct Methods in the Theory of Elliptic Equations
- An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation
- Asymptotic behavior of solution to the Cahn-Hillard equation
- 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
- Convergence of solutions to cahn-hilliard equation
- The Global Dynamics of Discrete Semilinear Parabolic Equations
- Counting stationary solutions of the Cahn–Hilliard equation by transversality arguments
- Numerical analysis of a model for phase separation of a multi-component alloy
- On the Cahn–Hilliard Equation with Degenerate Mobility
- On Modeling and Simulation of Electrokinetic Phenomena in Two-Phase Flow with General Mass Densities
- Finite Element Approximation of the Cahn--Hilliard Equation with Degenerate Mobility
- Weak Solutions of the Cahn--Hilliard System with Dynamic Boundary Conditions: A Gradient Flow Approach
- On Fully Decoupled, Convergent Schemes for Diffuse Interface Models for Two-Phase Flow with General Mass Densities
- On convergent schemes for two-phase flow of dilute polymeric solutions
- A variational approach to moving contact line hydrodynamics
- On Convergent Schemes for Diffuse Interface Models for Two-Phase Flow of Incompressible Fluids with General Mass Densities
- Stability Analysis of Large Time‐Stepping Methods for Epitaxial Growth Models
- Phase separation in confined geometries: Solving the Cahn-Hilliard equation with generic boundary conditions