Numerical Methods for Solving the Cahn–Hilliard Equation and Its Applicability to Related Energy-Based Models
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[1] Robert Nürnberg,et al. Adaptive finite element methods for Cahn-Hilliard equations , 2008 .
[2] Francisco Guillén-González,et al. Second order schemes and time-step adaptivity for Allen-Cahn and Cahn-Hilliard models , 2014, Comput. Math. Appl..
[3] J. Cahn,et al. A microscopic theory for antiphase boundary motion and its application to antiphase domain coasening , 1979 .
[4] Fatih Celiker,et al. Hybridizable Discontinuous Galerkin Methods for Timoshenko Beams , 2010, J. Sci. Comput..
[5] C. M. Elliott,et al. On the Cahn-Hilliard equation with degenerate mobility , 1996 .
[6] Jie Shen,et al. Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich-Schwoebel Type Energy: Application to Thin Film Epitaxy , 2012, SIAM J. Numer. Anal..
[7] James J. Feng,et al. A diffuse-interface method for simulating two-phase flows of complex fluids , 2004, Journal of Fluid Mechanics.
[8] D. Kwak,et al. Energetic variational approach in complex fluids: Maximum dissipation principle , 2009 .
[9] Sébastian Minjeaud. An unconditionally stable uncoupled scheme for a triphasic Cahn–Hilliard/Navier–Stokes model , 2013 .
[10] Santiago Badia,et al. Finite element approximation of nematic liquid crystal flows using a saddle-point structure , 2011, J. Comput. Phys..
[11] S. M. Wise,et al. Unconditionally Stable Finite Difference, Nonlinear Multigrid Simulation of the Cahn-Hilliard-Hele-Shaw System of Equations , 2010, J. Sci. Comput..
[12] F. Lin. Nonlinear theory of defects in nematic liquid crystals; Phase transition and flow phenomena , 1989 .
[13] Paul Papatzacos,et al. Diffuse-Interface Models for Two-Phase Flow , 2000 .
[14] C. M. Elliott,et al. Numerical Studies of the Cahn-Hilliard Equation for Phase Separation , 1987 .
[15] Vivette Girault,et al. Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms , 1986, Springer Series in Computational Mathematics.
[16] Juan Vicente Gutiérrez-Santacreu,et al. A linear mixed finite element scheme for a nematic Ericksen–Leslie liquid crystal model , 2013 .
[17] Franck Boyer,et al. Numerical schemes for a three component Cahn-Hilliard model , 2011 .
[18] Charles M. Elliott,et al. Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy , 1992 .
[19] Thomas J. R. Hughes,et al. Provably unconditionally stable, second-order time-accurate, mixed variational methods for phase-field models , 2011, J. Comput. Phys..
[20] C. M. Elliott,et al. A nonconforming finite-element method for the two-dimensional Cahn-Hilliard equation , 1989 .
[21] J. Waals. The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density , 1979 .
[22] Hui Zhang,et al. An energy law preserving C0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics , 2007, J. Comput. Phys..
[23] Q. Du,et al. Energetic variational approaches in modeling vesicle and fluid interactions , 2009 .
[24] Charles M. Elliott,et al. A second order splitting method for the Cahn-Hilliard equation , 1989 .
[25] Qiang Du,et al. Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions , 2006, J. Comput. Phys..
[26] Liyong Zhu,et al. ANALYSIS OF A MIXED FINITE ELEMENT METHOD FOR A PHASE FIELD BENDING ELASTICITY MODEL OF VESICLE , 2006 .
[27] R. Nicolaides,et al. Numerical analysis of a continuum model of phase transition , 1991 .
[28] Qi Wang,et al. Energy law preserving C0 finite element schemes for phase field models in two-phase flow computations , 2011, J. Comput. Phys..
[29] Junseok Kim,et al. Phase field computations for ternary fluid flows , 2007 .
[30] Qiang Du,et al. Convergence of numerical approximations to a phase field bending elasticity model of membrane deformations , 2006 .
[31] J. E. Hilliard,et al. Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .
[32] Q. Du,et al. A phase field approach in the numerical study of the elastic bending energy for vesicle membranes , 2004 .
[33] T. Hughes,et al. Isogeometric analysis of the Cahn–Hilliard phase-field model , 2008 .
[34] Qiang Du,et al. ANALYSIS OF A PHASE FIELD NAVIER-STOKES VESICLE-FLUID INTERACTION MODEL , 2007 .
[35] Xiaofeng Yang,et al. Numerical approximations of Allen-Cahn and Cahn-Hilliard equations , 2010 .
[36] Charles M. Elliott,et al. On the Cahn-Hilliard equation , 1986 .
[37] Chun Liu,et al. Simulations of singularity dynamics in liquid crystal flows: A C0 finite element approach , 2006, J. Comput. Phys..
[38] Olga Wodo,et al. Computationally efficient solution to the Cahn-Hilliard equation: Adaptive implicit time schemes, mesh sensitivity analysis and the 3D isoperimetric problem , 2011, J. Comput. Phys..
[39] Helmut Abels,et al. Strong Well-posedness of a Diffuse Interface Model for a Viscous, Quasi-incompressible Two-phase Flow , 2011, SIAM J. Math. Anal..
[40] H. Abels,et al. Thermodynamically Consistent, Frame Indifferent Diffuse Interface Models for Incompressible Two-Phase Flows with Different Densities , 2011, 1104.1336.
[41] P. Hohenberg,et al. Theory of Dynamic Critical Phenomena , 1977 .
[42] Francisco,et al. SPLITTING SCHEMES FOR A NAVIER-STOKES-CAHN-HILLIARD MODEL FOR TWO FLUIDS WITH DIFFERENT DENSITIES , 2014 .
[43] Junseok Kim,et al. CONSERVATIVE MULTIGRID METHODS FOR TERNARY CAHN-HILLIARD SYSTEMS ∗ , 2004 .
[44] Andreas Prohl,et al. Error analysis of a mixed finite element method for the Cahn-Hilliard equation , 2004, Numerische Mathematik.
[45] J. Lowengrub,et al. Conservative multigrid methods for Cahn-Hilliard fluids , 2004 .
[46] Daisuke Furihata,et al. A stable and conservative finite difference scheme for the Cahn-Hilliard equation , 2001, Numerische Mathematik.
[47] Franck Boyer,et al. A theoretical and numerical model for the study of incompressible mixture flows , 2002 .
[48] J. Lowengrub,et al. Quasi–incompressible Cahn–Hilliard fluids and topological transitions , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.
[49] Endre Süli,et al. Discontinuous Galerkin Finite Element Approximation of the Cahn-Hilliard Equation with Convection , 2009, SIAM J. Numer. Anal..
[50] Héctor D. Ceniceros,et al. TRACKING FLUID INTERFACES APPROACHING SINGULAR EVENTS , 2009 .
[51] L. Segel,et al. Nonlinear aspects of the Cahn-Hilliard equation , 1984 .
[52] Chun Liu,et al. Existence of Solutions for the Ericksen-Leslie System , 2000 .
[53] Stig Larsson,et al. THE CAHN-HILLIARD EQUATION , 2007 .
[54] Peter W. Bates,et al. The Dynamics of Nucleation for the Cahn-Hilliard Equation , 1993, SIAM J. Appl. Math..
[55] Francisco Guillén-González,et al. On linear schemes for a Cahn-Hilliard diffuse interface model , 2013, J. Comput. Phys..
[56] Junseok Kim,et al. Phase field modeling and simulation of three-phase flows , 2005 .
[57] F. Lin,et al. Nonparabolic dissipative systems modeling the flow of liquid crystals , 1995 .
[58] Harald Garcke,et al. Finite Element Approximation of the Cahn-Hilliard Equation with Degenerate Mobility , 1999, SIAM J. Numer. Anal..
[59] Jian Zhang,et al. Adaptive Finite Element Method for a Phase Field Bending Elasticity Model of Vesicle Membrane Deformations , 2008, SIAM J. Sci. Comput..
[60] Xiaobing Feng,et al. Fully Discrete Finite Element Approximations of the Navier-Stokes-Cahn-Hilliard Diffuse Interface Model for Two-Phase Fluid Flows , 2006, SIAM J. Numer. Anal..
[61] Yinnian He,et al. On large time-stepping methods for the Cahn--Hilliard equation , 2007 .
[62] E. Mello,et al. Numerical study of the Cahn–Hilliard equation in one, two and three dimensions , 2004, cond-mat/0410772.
[63] Junseok Kim. Phase-Field Models for Multi-Component Fluid Flows , 2012 .
[64] van der Kg Kristoffer Zee,et al. Stabilized second‐order convex splitting schemes for Cahn–Hilliard models with application to diffuse‐interface tumor‐growth models , 2014, International journal for numerical methods in biomedical engineering.
[65] Cheng Wang,et al. Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation , 2009, J. Comput. Phys..
[66] M. Gurtin,et al. TWO-PHASE BINARY FLUIDS AND IMMISCIBLE FLUIDS DESCRIBED BY AN ORDER PARAMETER , 1995, patt-sol/9506001.
[67] Andreas Prohl,et al. Finite Element Approximations of the Ericksen-Leslie Model for Nematic Liquid Crystal Flow , 2008, SIAM J. Numer. Anal..
[68] Jie Shen,et al. A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities , 2010, SIAM J. Sci. Comput..
[69] Harald Garcke,et al. Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities , 2011, Journal of Mathematical Fluid Mechanics.