Lumped finite elements for reaction-cross-diffusion systems on stationary surfaces
暂无分享,去创建一个
Anotida Madzvamuse | Chandrasekhar Venkataraman | Ivonne Sgura | Massimo Frittelli | C. Venkataraman | A. Madzvamuse | I. Sgura | Massimo Frittelli
[1] M. Schweizer,et al. Classical solutions to reaction-diffusion systems for hedging problems with interacting Ito and point processes , 2005, math/0505208.
[2] Vidar Thomée,et al. A Lumped Mass Finite-element Method with Quadrature for a Non-linear Parabolic Problem , 1985 .
[3] Mark A. J. Chaplain,et al. Robust numerical methods for taxis-diffusion-reaction systems: Applications to biomedical problems , 2006, Math. Comput. Model..
[4] C. Venkataraman,et al. Lumped finite element method for reaction-diffusion systems on compact surfaces , 2016, 1609.02741.
[5] Irving R Epstein,et al. Cross-diffusion and pattern formation in reaction-diffusion systems. , 2009, Physical chemistry chemical physics : PCCP.
[6] Weizhang Huang,et al. Maximum principle for the finite element solution of time‐dependent anisotropic diffusion problems , 2013 .
[7] Charles M. Elliott,et al. Finite element methods for surface PDEs* , 2013, Acta Numerica.
[8] Zoltán Horváth,et al. On Preservation of Positivity in Some Finite Element Methods for the Heat Equation , 2015, Comput. Methods Appl. Math..
[9] J. Smoller. Shock Waves and Reaction-Diffusion Equations , 1983 .
[10] Qiang Du,et al. Finite element approximation of the Cahn–Hilliard equation on surfaces , 2011 .
[11] Swarup Poria,et al. Turing patterns induced by cross-diffusion in a predator-prey system in presence of habitat complexity , 2016 .
[12] Anotida Madzvamuse,et al. Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations , 2015, Journal of mathematical biology.
[13] G. Dziuk. Finite Elements for the Beltrami operator on arbitrary surfaces , 1988 .
[14] David Hoff,et al. Stability and Convergence of Finite Difference Methods for Systems of Nonlinear Reaction-Diffusion Equations , 1978 .
[15] Sergey Korotov,et al. Discrete maximum principles for nonlinear parabolic PDE systems , 2012 .
[16] Rangarajan Sudarsan,et al. A Mixed-Culture Biofilm Model with Cross-Diffusion , 2015, Bulletin of Mathematical Biology.
[17] Jianxian Qiu,et al. Maximum principle in linear finite element approximations of anisotropic diffusion–convection–reaction problems , 2012, Numerische Mathematik.
[18] O. Annunziata,et al. Cross-diffusion in a colloid-polymer aqueous system , 2013 .
[19] A. Vergara,et al. Lysozyme Mutual Diffusion in Solutions Crowded by Poly(ethylene glycol) , 2006 .
[20] Alan J. Laub,et al. Matrix analysis - for scientists and engineers , 2004 .
[21] Ricardo H. Nochetto,et al. Combined effect of explicit time-stepping and quadrature for curvature driven flows , 1996 .
[22] Christian Lubich,et al. Variational discretization of wave equations on evolving surfaces , 2014, Math. Comput..
[23] Emmanuel Hebey,et al. Sobolev Spaces on Riemannian Manifolds , 1996 .
[24] Marcus R. Garvie,et al. Numerische Mathematik Finite element approximation of spatially extended predator – prey interactions with the Holling type II functional response , 2007 .
[25] Ansgar Jüngel,et al. Cross Diffusion Preventing Blow-Up in the Two-Dimensional Keller-Segel Model , 2011, SIAM J. Math. Anal..
[26] Charles M. Elliott,et al. L2-estimates for the evolving surface finite element method , 2012, Math. Comput..
[27] P. Bassanini,et al. Elliptic Partial Differential Equations of Second Order , 1997 .
[28] Rodrigo Ramos-Jiliberto,et al. Dynamic consequences of prey refuges in a simple model system: more prey, fewer predators and enhanced stability , 2003 .
[29] Bath Ba. THE GLOBAL DYNAMICS OF DISCRETE SEMILINEAR PARABOLIC EQUATIONS , 1993 .
[30] Charles M. Elliott,et al. Evolving surface finite element method for the Cahn–Hilliard equation , 2013, Numerische Mathematik.
[31] Omar Lakkis,et al. Implicit-Explicit Timestepping with Finite Element Approximation of Reaction-Diffusion Systems on Evolving Domains , 2011, SIAM J. Numer. Anal..
[32] Michael E. Taylor,et al. Partial Differential Equations III , 1996 .
[33] G. M.,et al. Partial Differential Equations I , 2023, Applied Mathematical Sciences.