The bulk-surface finite element method for reaction–diffusion systems on stationary volumes
Tài liệu tham khảo
W. Bangerth, T. Heister, L. Heltai, G. Kanschat, M. Kronbichler, M. Maier, B. Turcksin, T.D. Young, The deal.ii library, version 8.1. arXiv preprint arXiv:1312.2266, 2013.
Bänsch, 2000, Simulation of dendritic crystal growth with thermal convection, Interfaces Free Bound, 2, 95, 10.4171/IFB/14
Booty, 2010, A hybrid numerical method for interfacial fluid flow with soluble surfactant, J. Comput. Phys., 229, 3864, 10.1016/j.jcp.2010.01.032
E. Burman, P. Hansbo, M. Larson, S. Zahedi, Cut finite element methods for coupled bulk-surface problems, Numer. Math. (2014) doi:10.1007/s00211-015-0744-3.
Calhoun, 2009, A finite volume method for solving parabolic equations on logically cartesian curved surface meshes, SIAM J. Sci. Comput., 31, 4066, 10.1137/08073322X
Chechkin, 2012, Bulk-mediated diffusion on a planar surface, Phys. Rev. E, 86, 041101, 10.1103/PhysRevE.86.041101
Dziuk, 2007, Surface finite elements for parabolic equations, J. Comput. Math., 25, 385
Elliott, 2013, Finite element analysis for a coupled bulk-surface partial differential equation, IMA J. Numer. Anal., 33, 377, 10.1093/imanum/drs022
Elliott, 2012, Finite element analysis for a coupled bulk–surface partial differential equation, IMA J. Numer. Anal., 1
Gierer, 1972, A theory of biological pattern formation, Kybernetik, 12, 30, 10.1007/BF00289234
Greer, 2006, Fourth order partial differential equations on general geometries, J. Comput. Phys., 216, 216, 10.1016/j.jcp.2005.11.031
Gross, 2015, A trace finite element method for a class of coupled bulk-interface transport problems, ESAIM: Math. Modell. Numer. Anal., 9, 1303, 10.1051/m2an/2015013
Heys, 2004, First-order system least squares (fosls) for coupled fluid-elastic problems, J. Comput. Phys., 195, 560, 10.1016/j.jcp.2003.09.034
Hieber, 2005, A Lagrangian particle level set method, J. Comput. Phys., 210, 342, 10.1016/j.jcp.2005.04.013
Jaffe, 2005, Rho gtpases, Annu. Rev. Cell Dev. Biol., 21, 247, 10.1146/annurev.cellbio.21.020604.150721
Murray, 2003
D. Köster, O. Kriessl, K.G. Siebert, Design of Finite Element Tools for Coupled Surface and Volume Meshes, Technical Report 2008-01, Mathematik, 2008.
Macdonald, 2013, Simple computation of reaction–diffusion processes on point clouds, Proc. Natl. Acad. Sci., 110, 9209, 10.1073/pnas.1221408110
Macdonald, 2009, The implicit closest point method for the numerical solution of partial differential equations on surfaces, SIAM J. Sci. Comput., 31, 4330, 10.1137/080740003
Madzvamuse, 2014, Fully implicit time-stepping schemes and non-linear solvers for systems of reaction–diffusion equations, Appl. Math. Comput., 244, 361, 10.1016/j.amc.2014.07.004
Madzvamuse, 2015, Stability analysis and simulations of coupled bulk-surface reaction–diffusion systems, Proc. R. Soc. A, 471
Medvedev, 2013, Mechanism of long-range proton translocation along biological membranes, FEBS Lett., 587, 345, 10.1016/j.febslet.2012.12.010
Nisbet, 2009, Surface and bulk characterisation of electrospun membranes, Colloids Surf. B, 71, 1, 10.1016/j.colsurfb.2009.01.022
Novak, 2007, Diffusion on a curved surface coupled to diffusion in the volume: application to cell biology, J. Comput. Phys., 226, 1271, 10.1016/j.jcp.2007.05.025
Prigogine, 1968, Symmetry breaking instabilities in dissipative systems. ii, J. Chem. Phys., 48, 1695, 10.1063/1.1668896
Rätz, 2012, Turing instabilities in a mathematical model for signaling networks, J. Math. Biol., 65, 1215, 10.1007/s00285-011-0495-4
Rätz, 2014, Symmetry breaking in a bulk-surface reaction–diffusion model for signaling networks, Nonlinearity, 27, 1805, 10.1088/0951-7715/27/8/1805
Schnakenberg, 1979, Simple chemical reaction systems with limit cycle behaviour, J. Theor. Biol., 81, 389, 10.1016/0022-5193(79)90042-0
Turing, 1952, The chemical basis of morphogenesis, Philos. Trans. R. Soc. B, 237, 37, 10.1098/rstb.1952.0012