Superconvergent second order Cartesian method for solving free boundary problem for invadopodia formation
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[1] So-Hsiang Chou,et al. Superconvergence of finite volume methods for the second order elliptic problem , 2007 .
[2] R. F. Warming,et al. Upwind Second-Order Difference Schemes and Applications in Aerodynamic Flows , 1976 .
[3] A. Friedman. Variational principles and free-boundary problems , 1982 .
[4] Ronald Fedkiw,et al. Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.
[5] R. Fedkiw,et al. A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem , 2005 .
[6] P. P. Starling. The numerical solution of Laplace's equation , 1963 .
[7] Siegfried M. Rump,et al. Symbolic Algebraic Methods and Verification Methods , 2001 .
[8] Li-Tien Cheng,et al. A second-order-accurate symmetric discretization of the Poisson equation on irregular domains , 2002 .
[9] Stanley Osher,et al. A Hybrid Method for Moving Interface Problems with Application to the Hele-Shaw Flow , 1997 .
[10] Shilpa Khatri,et al. An embedded boundary method for soluble surfactants with interface tracking for two-phase flows , 2014, J. Comput. Phys..
[11] Olivier Gallinato,et al. Modélisation de processus cancéreux et méthodes superconvergentes de résolution de problèmes d'interface sur grille cartésienne. (Modeling of cancer phenomena and superconvergent methods for the resolution of interface problems on Cartesian grid) , 2016 .
[12] Miloš Zlámal,et al. Superconvergence and reduced integration in the finite element method , 1978 .
[13] James A. Sethian,et al. The Fast Construction of Extension Velocities in Level Set Methods , 1999 .
[14] Song Wang,et al. Superconvergence of solution derivatives of the Shortley--Weller difference approximation to Poisson's equation with singularities on polygonal domains , 2008 .
[15] T. Chan,et al. A Variational Level Set Approach to Multiphase Motion , 1996 .
[16] C. Poignard,et al. Free boundary problem for cell protrusion formations: theoretical and numerical aspects , 2017, Journal of mathematical biology.
[17] Nami Matsunaga,et al. Superconvergence of the Shortley-Weller approximation for Dirichlet problems , 2000 .
[18] Frédéric Gibou,et al. A supra-convergent finite difference scheme for the variable coefficient Poisson equation on non-graded grids , 2006, J. Comput. Phys..
[19] J. Sethian,et al. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .
[20] Chohong Min,et al. A REVIEW OF THE SUPRA-CONVERGENCES OF SHORTLEY-WELLER METHOD FOR POISSON EQUATION , 2014 .
[21] O. Bruno,et al. Numerical Differentiation of Approximated Functions with Limited Order-of-Accuracy Deterioration , 2012, SIAM J. Numer. Anal..
[22] Qing Fang,et al. Superconvergence of solution derivatives for the Shortley-Weller difference approximation of Poisson's equation. Part I: smoothness problems , 2003 .
[23] C. Macaskill,et al. The Shortley-Weller embedded finite-difference method for the 3D Poisson equation with mixed boundary conditions , 2010, J. Comput. Phys..
[24] John E. Osborn,et al. Superconvergence in the generalized finite element method , 2007, Numerische Mathematik.
[25] S. Osher,et al. A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method) , 1999 .
[26] Rolf Dieter Grigorieff,et al. On the supraconvergence of elliptic finite difference schemes , 1998 .
[27] Philippe G. Ciarlet. Discrete maximum principle for finite-difference operators , 1970 .
[28] Gang-Joon Yoon,et al. Convergence Analysis of the Standard Central Finite Difference Method for Poisson Equation , 2016, J. Sci. Comput..
[29] M. Cisternino,et al. A Parallel Second Order Cartesian Method for Elliptic Interface Problems , 2012 .
[30] Heinz-Otto Kreiss,et al. Difference Approximations of the Neumann Problem for the Second Order Wave Equation , 2004, SIAM J. Numer. Anal..
[31] Qing Fang,et al. Superconvergence of Solution Derivatives for the Shortley–Weller Difference Approximation of Poisson's Equation. II. Singularity Problems , 2003 .
[32] Frédéric Gibou,et al. A numerical scheme for the Stefan problem on adaptive Cartesian grids with supralinear convergence rate , 2009, J. Comput. Phys..
[33] Frédéric Gibou,et al. A Supra-Convergent Finite Difference Scheme for the Poisson and Heat Equations on Irregular Domains and Non-Graded Adaptive Cartesian Grids , 2007, J. Sci. Comput..
[34] Chunjia Bi,et al. Superconvergence of finite volume element method for a nonlinear elliptic problem , 2007 .
[35] Erwan Deriaz,et al. Stability Conditions for the Numerical Solution of Convection-Dominated Problems with Skew-Symmetric Discretizations , 2010, SIAM J. Numer. Anal..
[36] S. Osher,et al. Algorithms Based on Hamilton-Jacobi Formulations , 1988 .
[37] Frédéric Gibou,et al. Efficient symmetric discretization for the Poisson, heat and Stefan-type problems with Robin boundary conditions , 2010, J. Comput. Phys..
[38] Olivier Gallinato Contino. Modeling of cancer phenomena and superconvergent methods for the resolution of interface problems on Cartesian grid. (Modélisation de processus cancéreux et méthodes superconvergentes de résolution de problèmes d'interface sur grille cartésienne) , 2016 .
[39] Nick Levine,et al. Superconvergent Recovery of the Gradient from Piecewise Linear Finite-element Approximations , 1985 .
[40] B. E. Hubbard,et al. On the formulation of finite difference analogues of the Dirichlet problem for Poisson's equation , 1962 .
[41] Tie Zhang,et al. The gradient superconvergence of the finite volume method for a nonlinear elliptic problem of nonmonotone type , 2015 .