Efficient and accurate structure preserving schemes for complex nonlinear systems
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[1] Jie Shen,et al. A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method , 2003 .
[2] M. Gurtin,et al. TWO-PHASE BINARY FLUIDS AND IMMISCIBLE FLUIDS DESCRIBED BY AN ORDER PARAMETER , 1995, patt-sol/9506001.
[3] Q. Du,et al. The phase field method for geometric moving interfaces and their numerical approximations , 2019, Geometric Partial Differential Equations - Part I.
[4] Suchuan Dong,et al. Numerical approximation of incompressible Navier-Stokes equations based on an auxiliary energy variable , 2018, J. Comput. Phys..
[5] S. Edwards,et al. The Theory of Polymer Dynamics , 1986 .
[6] Zhiping Mao,et al. Analysis and Approximation of a Fractional Cahn-Hilliard Equation , 2017, SIAM J. Numer. Anal..
[7] Shuyu Sun,et al. Decoupled, energy stable schemes for a phase-field surfactant model , 2018, Comput. Phys. Commun..
[8] Axel Voigt,et al. A new phase-field model for strongly anisotropic systems , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[9] Jie Shen,et al. Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows , 2018, SIAM J. Numer. Anal..
[10] R. Larson. Arrested Tumbling in Shearing Flows of Liquid Crystal Polymers , 1990 .
[11] Xiaofeng Yang,et al. Numerical approximations for a phase field dendritic crystal growth model based on the invariant energy quadratization approach , 2017 .
[12] M. Gregory Forest,et al. The weak shear kinetic phase diagram for nematic polymers , 2004 .
[13] J. Cahn,et al. A microscopic theory for antiphase boundary motion and its application to antiphase domain coasening , 1979 .
[14] Felix Otto,et al. Lubrication approximation with prescribed nonzero contact anggle , 1998 .
[15] Jie Shen,et al. Highly Efficient and Accurate Numerical Schemes for the Epitaxial Thin Film Growth Models by Using the SAV Approach , 2019, J. Sci. Comput..
[16] Jie Shen,et al. Efficient SAV approach for imaginary time gradient flows with applications to one- and multi-component Bose-Einstein Condensates , 2019, J. Comput. Phys..
[17] Ricardo H. Nochetto,et al. A posteriori error control for the Allen–Cahn problem: circumventing Gronwall's inequality , 2004 .
[18] James J. Feng,et al. A diffuse-interface method for simulating two-phase flows of complex fluids , 2004, Journal of Fluid Mechanics.
[19] 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.
[20] Xiaofeng Yang,et al. Energy stable schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows , 2010 .
[21] Zhangxin Chen,et al. Efficient Linearly and Unconditionally Energy Stable Schemes for the Phase Field Model of Solid-State Dewetting Problems , 2018, ICCS.
[22] Q. Du,et al. A phase field approach in the numerical study of the elastic bending energy for vesicle membranes , 2004 .
[23] R. Nicolaides,et al. Numerical analysis of a continuum model of phase transition , 1991 .
[24] S. Dong,et al. An unconditionally energy-stable scheme based on an implicit auxiliary energy variable for incompressible two-phase flows with different densities involving only precomputable coefficient matrices , 2018, J. Comput. Phys..
[25] Qing Cheng,et al. Multiple Scalar Auxiliary Variable (MSAV) Approach and its Application to the Phase-Field Vesicle Membrane Model , 2018, SIAM J. Sci. Comput..
[26] Lorenzo Giacomelli,et al. Variatonal formulation for the lubrication approximation of the Hele-Shaw flow , 2001 .
[27] Shuyu Sun,et al. Linearly Decoupled Energy-Stable Numerical Methods for Multicomponent Two-Phase Compressible Flow , 2018, SIAM J. Numer. Anal..
[28] Yongzhong Song,et al. Structure-preserving algorithms for the two-dimensional sine-Gordon equation with Neumann boundary conditions , 2018, J. Comput. Phys..
[29] Xiaofeng Yang,et al. Numerical approximations of Allen-Cahn and Cahn-Hilliard equations , 2010 .
[30] J. E. Hilliard,et al. Free Energy of a Nonuniform System. I. Interfacial Free Energy and Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid , 2013 .
[31] Endre Süli,et al. Spectral approximation of pattern-forming nonlinear evolution equations with double-well potentials of quadratic growth , 2010, Math. Comput..
[32] J. E. Hilliard,et al. Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .
[33] M. Gregory Forest,et al. The flow-phase diagram of Doi-Hess theory for sheared nematic polymers II: finite shear rates , 2004 .
[34] F. M. Leslie. Theory of Flow Phenomena in Liquid Crystals , 1979 .
[35] Thomas J. R. Hughes,et al. Provably unconditionally stable, second-order time-accurate, mixed variational methods for phase-field models , 2011, J. Comput. Phys..
[36] Jie Shen,et al. On the maximum principle preserving schemes for the generalized Allen–Cahn equation , 2016 .
[37] Junseok Kim. Phase-Field Models for Multi-Component Fluid Flows , 2012 .
[38] Desai,et al. Numerical study of late-stage coarsening for off-critical quenches in the Cahn-Hilliard equation of phase separation. , 1989, Physical review. B, Condensed matter.
[39] Jiang Yang,et al. The scalar auxiliary variable (SAV) approach for gradient flows , 2018, J. Comput. Phys..
[40] Jie Shen,et al. A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows , 2017, SIAM Rev..
[41] Pingwen Zhang,et al. A Nonhomogeneous Kinetic Model of Liquid Crystal Polymers and Its Thermodynamic Closure Approximation , 2009 .
[42] D. M. Anderson,et al. DIFFUSE-INTERFACE METHODS IN FLUID MECHANICS , 1997 .
[43] Xiaofeng Yang,et al. Efficient schemes with unconditionally energy stability for the anisotropic Cahn-Hilliard Equation using the stabilized-Scalar Augmented Variable (S-SAV) approach , 2018, 1804.02619.
[44] Jie Shen,et al. Energy stability and convergence of SAV block-centered finite difference method for gradient flows , 2018, Math. Comput..
[45] John E. Hilliard,et al. Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid , 1959 .
[46] Xiaofeng Yang,et al. Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends , 2016, J. Comput. Phys..
[47] L. Rudin,et al. Nonlinear total variation based noise removal algorithms , 1992 .