An adaptive discontinuous finite volume element method for the Allen-Cahn equation

[1]  Cheng Wang,et al.  A Third Order Accurate in Time, BDF-Type Energy Stable Scheme for the Cahn-Hilliard Equation , 2022, Numerical Mathematics: Theory, Methods and Applications.

[2]  Steven M. Wise,et al.  An improved error analysis for a second-order numerical scheme for the Cahn-Hilliard equation , 2021, J. Comput. Appl. Math..

[3]  Gregory A. Hackett,et al.  Phase field simulation of anode microstructure evolution of solid oxide fuel cell through Ni(OH)2 diffusion , 2021 .

[4]  Xiaofeng Yang.  A novel fully decoupled scheme with second‐order time accuracy and unconditional energy stability for the Navier‐Stokes equations coupled with mass‐conserved Allen‐Cahn phase‐field model of two‐phase incompressible flow , 2020, International Journal for Numerical Methods in Engineering.

[5]  Yaoyao Chen,et al.  Recovery type a posteriori error estimation of adaptive finite element method for Allen-Cahn equation , 2020, J. Comput. Appl. Math..

[6]  Somnath Ghosh,et al.  A coupled crystal plasticity FEM and phase-field model for crack evolution in microstructures of 7000 series aluminum alloys , 2020 .

[7]  G. Górski,et al.  Two-phase flow pattern identification in minichannels using image correlation analysis , 2020 .

[8]  R. Meher,et al.  Modelling of counter current imbibition phenomenon in two-phase fluid flows through fractured heterogeneous porous media under the effect of magnetic field , 2020 .

[9]  Xiaoming He,et al.  Discontinuous finite volume element method for a coupled Navier-Stokes-Cahn-Hilliard phase field model , 2020, Adv. Comput. Math..

[10]  Hector Gomez,et al.  Phase-field model of vascular tumor growth: Three-dimensional geometry of the vascular network and integration with imaging data , 2020 .

[11]  Shi Yi,et al.  A phase field method for the numerical simulation of rigid particulate in two-phase flows , 2020 .

[12]  Jun Zhang,et al.  Efficient, non-iterative, and second-order accurate numerical algorithms for the anisotropic Allen-Cahn Equation with precise nonlocal mass conservation , 2020, J. Comput. Appl. Math..

[13]  Xiaoming He,et al.  Fast, unconditionally energy stable large time stepping method for a new Allen-Cahn type square phase-field crystal model , 2019, Appl. Math. Lett..

[14]  Buyang Li,et al.  Energy-Decaying Extrapolated RK-SAV Methods for the Allen-Cahn and Cahn-Hilliard Equations , 2019, SIAM J. Sci. Comput..

[15]  Shuangshuang Chen,et al.  A discontinuous finite volume method for a coupled fracture model , 2019, Comput. Math. Appl..

[16]  Xiaoming He,et al.  A diffuse interface model and semi-implicit energy stable finite element method for two-phase magnetohydrodynamic flows , 2019, Computer Methods in Applied Mechanics and Engineering.

[17]  Chongmin Song,et al.  Adaptive phase-field modeling of brittle fracture using the scaled boundary finite element method , 2019, Computer Methods in Applied Mechanics and Engineering.

[18]  X. Niu,et al.  A diffuse interface lattice Boltzmann model for thermocapillary flows with large density ratio and thermophysical parameters contrasts , 2019, International Journal of Heat and Mass Transfer.

[19]  Yaoyao Chen,et al.  A SCR-based error estimation and adaptive finite element method for the Allen-Cahn equation , 2019, Comput. Math. Appl..

[20]  M. Liang,et al.  Phase field simulation and microscopic observation of phase separation and thermal stability of polymer modified asphalt , 2019, Construction and Building Materials.

[21]  Zhenhui He,et al.  The preparation of AgI/Au/foam-Cu as a framework of composite for water-based cool storage phase-change material with low supercooling , 2019, Thermochimica Acta.

[22]  Yi Zhang,et al.  Fully Discrete Mixed Finite Element Methods for the Stochastic Cahn-Hilliard Equation with Gradient-type Multiplicative Noise , 2019, 1903.05146.

[23]  Wenbin Chen,et al.  A Second Order BDF Numerical Scheme with Variable Steps for the Cahn-Hilliard Equation , 2019, SIAM J. Numer. Anal..

[24]  Jie Shen,et al.  Energy stability and convergence of SAV block-centered finite difference method for gradient flows , 2018, Math. Comput..

[25]  Guirong Liu,et al.  A phase-field modeling for brittle fracture and crack propagation based on the cell-based smoothed finite element method , 2018, Engineering Fracture Mechanics.

[26]  Peter Wriggers,et al.  Phase-field modeling of brittle fracture using an efficient virtual element scheme , 2018, Computer Methods in Applied Mechanics and Engineering.

[27]  Yang Li,et al.  Axisymmetric lattice Boltzmann model for multiphase flows with large density ratio , 2018, International Journal of Heat and Mass Transfer.

[28]  C. Mascia,et al.  Kinetic schemes for assessing stability of traveling fronts for the Allen–Cahn equation with relaxation , 2018, Applied Numerical Mathematics.

[29]  Peter K. Jimack,et al.  Dynamic Load Balancing for the Parallel, Adaptive, Multigrid Solution of Implicit Phase-Field Simulations , 2018 .

[30]  Zhangxin Chen,et al.  Discontinuous Finite Volume Element Method for a Coupled Non-stationary Stokes–Darcy Problem , 2018, J. Sci. Comput..

[31]  Xiaoming He,et al.  Decoupled, Linear, and Energy Stable Finite Element Method for the Cahn-Hilliard-Navier-Stokes-Darcy Phase Field Model , 2018, SIAM J. Sci. Comput..

[32]  Jiang Yang,et al.  The scalar auxiliary variable (SAV) approach for gradient flows , 2018, J. Comput. Phys..

[33]  Wenqiang Feng,et al.  An energy stable fourth order finite difference scheme for the Cahn-Hilliard equation , 2017, J. Comput. Appl. Math..

[34]  Xiaoming He,et al.  A stabilized finite volume element method for a coupled Stokes–Darcy problem , 2017, Applied Numerical Mathematics.

[35]  Christian Engwer,et al.  A phase field approach to pressurized fractures using discontinuous Galerkin methods , 2017, Math. Comput. Simul..

[36]  Xiaoming He,et al.  Three dimensional phase-field investigation of droplet formation in microfluidic flow focusing devices with experimental validation , 2017 .

[37]  Ricardo Ruiz-Baier,et al.  Discontinuous finite volume element methods for the optimal control of Brinkman equations , 2017 .

[38]  Z. G. Xu,et al.  Numerical study of solid-liquid phase change by phase field method , 2017 .

[39]  Rui Li,et al.  Discontinuous Finite Volume Element Method for a Coupled Non-stationary Stokes–Darcy Problem , 2017, Journal of Scientific Computing.

[40]  Tie Zhang,et al.  A Discontinuous Finite Volume Element Method Based on Bilinear Trial Functions , 2017 .

[41]  Xiaoming He,et al.  Linear, second order and unconditionally energy stable schemes for the viscous Cahn-Hilliard equation with hyperbolic relaxation using the invariant energy quadratization method , 2017, J. Comput. Appl. Math..

[42]  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..

[43]  Cheng Wang,et al.  A Second-Order, Weakly Energy-Stable Pseudo-spectral Scheme for the Cahn–Hilliard Equation and Its Solution by the Homogeneous Linear Iteration Method , 2016, J. Sci. Comput..

[44]  Beatrice Riviere,et al.  A finite volume / discontinuous Galerkin method for the advective Cahn–Hilliard equation with degenerate mobility on porous domains stemming from micro-CT imaging , 2016, Computational Geosciences.

[45]  Xiaohu Lu,et al.  Modelling and numerical simulation of phase separation in polymer modified bitumen by phase-field method , 2016 .

[46]  Yinnian He,et al.  Discontinuous finite volume methods for the stationary Stokes–Darcy problem , 2016 .

[47]  Cheng Wang,et al.  Convergence analysis and error estimates for a second order accurate finite element method for the Cahn–Hilliard–Navier–Stokes system , 2016, Numerische Mathematik.

[48]  Shuonan Wu,et al.  On the stability and accuracy of partially and fully implicit schemes for phase field modeling , 2016, Computer Methods in Applied Mechanics and Engineering.

[49]  Ying Chen,et al.  Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models , 2016, J. Comput. Phys..

[50]  Yan Xu,et al.  Interior Penalty Discontinuous Galerkin Based Isogeometric Analysis for Allen-Cahn Equations on Surfaces , 2015 .

[51]  Jaemin Shin,et al.  First and second order operator splitting methods for the phase field crystal equation , 2015, J. Comput. Phys..

[52]  Jie Shen,et al.  Decoupled, Energy Stable Schemes for Phase-Field Models of Two-Phase Incompressible Flows , 2015, SIAM J. Numer. Anal..

[53]  Amanda E. Diegel,et al.  Stability and Convergence of a Second Order Mixed Finite Element Method for the Cahn-Hilliard Equation , 2014, 1411.5248.

[54]  M. Uzunca,et al.  Energy Stable Discontinuous Galerkin Finite Element Method for the Allen-Cahn Equation , 2014, 1409.3997.

[55]  Xiaoming Wang,et al.  A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn-Hilliard-Navier-Stokes equation , 2014, J. Comput. Phys..

[56]  Danielle Hilhorst,et al.  On a Cahn-Hilliard type phase field system related to tumor growth , 2014, 1401.5943.

[57]  Xiaobing Feng,et al.  Analysis of interior penalty discontinuous Galerkin methods for the Allen-Cahn equation and the mean curvature flow , 2013, 1310.7504.

[58]  T. Tang,et al.  Nonlinear stability of the implicit-explicit methods for the Allen-Cahn equation , 2013 .

[59]  Amir R. Khoei,et al.  An extended finite element method for fluid flow in partially saturated porous media with weak discontinuities; the convergence analysis of local enrichment strategies , 2013 .

[60]  Zhangxin Chen,et al.  On the semi-discrete stabilized finite volume method for the transient Navier–Stokes equations , 2013, Adv. Comput. Math..

[61]  Xinlong Feng,et al.  Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models , 2013 .

[62]  Qiang Xu,et al.  A Discontinuous Finite Volume Method for the Darcy-Stokes Equations , 2012, J. Appl. Math..

[63]  Zhangxin Chen,et al.  A stabilized multi-level method for non-singular finite volume solutions of the stationary 3D Navier–Stokes equations , 2012, Numerische Mathematik.

[64]  Chunjia Bi,et al.  A discontinuous finite volume element method for second‐order elliptic problems , 2012 .

[65]  Min Gao,et al.  A gradient stable scheme for a phase field model for the moving contact line problem , 2012, J. Comput. Phys..

[66]  Qi Wang,et al.  Energy law preserving C0 finite element schemes for phase field models in two-phase flow computations , 2011, J. Comput. Phys..

[67]  Lin Mu,et al.  An adaptive discontinuous finite volume method for elliptic problems , 2011, J. Comput. Appl. Math..

[68]  Junseok Kim,et al.  A fast, robust, and accurate operator splitting method for phase-field simulations of crystal growth , 2011 .

[69]  K. Elder,et al.  The Kirkendall effect in the phase field crystal model , 2011 .

[70]  Charles M. Elliott,et al.  Modeling and computation of two phase geometric biomembranes using surface finite elements , 2010, J. Comput. Phys..

[71]  Zhangxin Chen,et al.  Convergence and stability of a stabilized finite volume method for the stationary Navier-Stokes equations , 2010 .

[72]  Xiaofeng Yang,et al.  Numerical approximations of Allen-Cahn and Cahn-Hilliard equations , 2010 .

[73]  V. Levitas,et al.  Interface Propagation and Microstructure Evolution in Phase Field Models of Stress-Induced Martensitic Phase Transformations , 2010 .

[74]  Chunjia Bi,et al.  Discontinuous finite volume element method for parabolic problems , 2010 .

[75]  Xiaofeng Yang,et al.  Error analysis of stabilized semi-implicit method of Allen-Cahnequation , 2009 .

[76]  Zhangxin Chen,et al.  A new stabilized finite volume method for the stationary Stokes equations , 2009, Adv. Comput. Math..

[77]  T. Takaki,et al.  Phase-Field Modeling and Simulation of Nucleation and Growth of Recrystallized Grains , 2007 .

[78]  Huazhong Tang,et al.  An adaptive phase field method for the mixture of two incompressible fluids , 2007 .

[79]  So-Hsiang Chou,et al.  Unified Analysis of Finite Volume Methods for Second Order Elliptic Problems , 2007, SIAM J. Numer. Anal..

[80]  Xiaobing Feng,et al.  Fully discrete dynamic mesh discontinuous Galerkin methods for the Cahn-Hilliard equation of phase transition , 2007, Math. Comput..

[81]  Philippe Angot,et al.  A finite element penalty-projection method for incompressible flows , 2006, J. Comput. Phys..

[82]  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..

[83]  J. Herndon.  Solar System Processes Underlying Planetary Formation, Geodynamics, and the Georeactor , 2006, astro-ph/0602232.

[84]  Xiu Ye,et al.  A Discontinuous Finite Volume Method for the Stokes Problems , 2006, SIAM J. Numer. Anal..

[85]  H. Nakanishi,et al.  Phase Field Model for Dynamics of Sweeping Interface , 2005, cond-mat/0503383.

[86]  Jie Shen,et al.  A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method , 2003 .

[87]  Andreas Prohl,et al.  Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows , 2003, Numerische Mathematik.

[88]  A. A. Merkin,et al.  Analysis of the amplitude and phase structure of transmitting media with probing field registration in the image plane , 2002 .

[89]  A. Karma,et al.  Phase-Field Simulation of Solidification , 2002 .

[90]  W. Carter,et al.  A continuum model of grain boundaries , 2000 .

[91]  Long-Qing Chen,et al.  COMPUTER SIMULATION OF GRAIN GROWTH USING A CONTINUUM FIELD MODEL , 1997 .

[92]  I. Steinbach,et al.  A phase field concept for multiphase systems , 1996 .

[93]  R. Nicolaides,et al.  Numerical analysis of a continuum model of phase transition , 1991 .

[94]  J. Cahn,et al.  A microscopic theory for antiphase boundary motion and its application to antiphase domain coasening , 1979 .

[95]  Jianhua Wu,et al.  Discontinuous finite volume element method for Darcy flows in fractured porous media , 2021, J. Comput. Appl. Math..

[96]  Xiaoming He,et al.  Numerical approximations for the hydrodynamics coupled binary surfactant phase field model: Second-order, linear, unconditionally energy-stable schemes , 2019, Communications in Mathematical Sciences.

[97]  Peter Wriggers,et al.  VIRTUAL ELEMENT FORMULATION FOR PHASE-FIELD MODELING OF DUCTILE FRACTURE , 2019, International Journal for Multiscale Computational Engineering.

[98]  Cheng Wang,et al.  A Second-Order Energy Stable BDF Numerical Scheme for the Cahn-Hilliard Equation , 2018 .

[99]  L. Rebholz.  PENALTY-PROJECTION SCHEMES FOR THE CAHN-HILLIARD NAVIER-STOKES DIFFUSE INTERFACE MODEL OF TWO PHASE FLOW , AND THEIR CONNECTION TO DIVERGENCE-FREE COUPLED SCHEMES , 2018 .

[100]  Jiang Yang,et al.  UNIFORM L p -BOUND OF THE ALLEN–CAHN EQUATION AND ITS NUMERICAL DISCRETIZATION , 2017 .

[101]  Cheng Wang,et al.  An $H^2$ convergence of a second-order convex-splitting, finite difference scheme for the three-dimensional Cahn–Hilliard equation , 2016 .

[102]  Zhangxin Chen,et al.  Optimal $$L^2, H^1$$L2,H1 and $$L^\infty $$L∞ analysis of finite volume methods for the stationary Navier–Stokes equations with large data , 2014, Numerische Mathematik.

[103]  Numerische,et al.  Optimal L 2 , H 1 and L ∞ analysis of finite volume methods for the stationary Navier–Stokes equations with large data , 2013 .

[104]  Zhang Kun.  The discontinuous finite volume element method for parabolic and hyperbolic equations , 2012 .

[105]  Zhangxin Chen,et al.  ANALYSIS OF A STABILIZED FINITE VOLUME METHOD FOR THE TRANSIENT STOKES EQUATIONS , 2009 .

[106]  S. Esedoglu,et al.  Threshold dynamics for the piecewise constant Mumford-Shah functional , 2006 .

[107]  Xiu Ye,et al.  A New Discontinuous Finite Volume Method for Elliptic Problems , 2004, SIAM J. Numer. Anal..

[108]  T. Belytschko,et al.  An Extended Finite Element Method for Two-Phase Fluids , 2003 .

[109]  Lin Mu,et al.  Journal of Computational and Applied Mathematics Convergence of the Discontinuous Finite Volume Method for Elliptic Problems with Minimal Regularity , 2022 .