Error estimate of the finite volume scheme for the Allen–Cahn equation

[1]  P. Strachota,et al.  Design and Verification of the MPFA Scheme for Three-Dimensional Phase Field Model of Dendritic Crystal Growth , 2013 .

[2]  Pavel Strachota,et al.  Towards clinical applicability of the diffusion-based DT-MRI visualization algorithm , 2012, J. Vis. Commun. Image Represent..

[3]  Peter K. Jimack,et al.  An adaptive, multilevel scheme for the implicit solution of three‐dimensional phase‐field equations , 2011 .

[4]  Harald Garcke,et al.  On stable parametric finite element methods for the Stefan problem and the Mullins-Sekerka problem with applications to dendritic growth , 2010, J. Comput. Phys..

[5]  K. Mikula,et al.  Error estimates of the finite volume scheme for the nonlinear tensor-driven anisotropic diffusion , 2009 .

[6]  Olga Stasová,et al.  Convergence Analysis of Finite Volume Scheme for Nonlinear Tensor Anisotropic Diffusion in Image Processing , 2007, SIAM J. Numer. Anal..

[7]  Meie Li,et al.  Growth morphologies of a binary alloy with low anisotropy in directional solidification , 2007 .

[8]  M. Beneš.  Computational studies of anisotropic diffuse interface model of microstructure formation in solidification , 2007 .

[9]  G. Amberg,et al.  Morphology diagram of thermal dendritic solidification by means of phase-field models in two and three dimensions , 2006 .

[10]  J. Butcher.  Numerical Methods for Ordinary Differential Equations: Butcher/Numerical Methods , 2005 .

[11]  Michal Beneš,et al.  Diffuse-Interface Treatment of the Anisotropic Mean-Curvature Flow , 2003 .

[12]  J. Butcher.  Numerical methods for ordinary differential equations , 2003 .

[13]  R. Cochrane,et al.  A phase field model for spontaneous grain refinement in deeply undercooled metallic melts , 2001 .

[14]  Michal Beneš,et al.  Mathematical analysis of phase-field equations with numerically efficient coupling terms , 2001 .

[15]  N. Goldenfeld,et al.  Phase field model for three-dimensional dendritic growth with fluid flow. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  R. Eymard,et al.  Finite Volume Methods , 2019, Computational Methods for Fluid Dynamics.

[17]  Yves Coudière,et al.  CONVERGENCE RATE OF A FINITE VOLUME SCHEME FOR A TWO DIMENSIONAL CONVECTION-DIFFUSION PROBLEM , 1999 .

[18]  N. Goldenfeld,et al.  Adaptive Mesh Refinement Computation of Solidification Microstructures Using Dynamic Data Structures , 1998, cond-mat/9808216.

[19]  W. Rappel,et al.  Numerical Simulation of Three-Dimensional Dendritic Growth. , 1996, Physical review letters.

[20]  A. Schmidt.  Computation of Three Dimensional Dendrites with Finite Elements , 1996 .

[21]  A. Karma,et al.  Quantitative phase-field modeling of dendritic growth in two and three dimensions , 1996 .

[22]  Ben-Jacob,et al.  Numerical study of a morphology diagram in the large undercooling limit using a phase-field model. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  Ricardo H. Nochetto,et al.  An Adaptive Finite Element Method for Two-Phase Stefan Problems in Two Space Dimensions. II: Implementation and Numerical Experiments , 1991, SIAM J. Sci. Comput..

[24]  Ricardo H. Nochetto,et al.  AN ADAPTIVE FINITE ELEMENT METHOD FOR TWO-PHASE STEFAN PROBLEMS IN TWO SPACE DIMENSIONS. PART I: STABILITY AND ERROR ESTIMATES , 1991 .

[25]  F. Brauer,et al.  The Qualitative Theory of Ordinary Differential Equations: An Introduction , 1989 .

[26]  Karel Rektorys,et al.  The method of discretization in time and partial differential equations , 1982 .

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

[28]  Witold Hurewicz,et al.  Lectures on Ordinary Differential Equations , 1959 .