caa a22 4500 445329866 CHVBK 20180317142733.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00285-011-0401-0 doi (NATIONALLICENCE)springer-10.1007/s00285-011-0401-0 The surface finite element method for pattern formation on evolving biological surfaces [Elektronische Daten] [R. Barreira, C. Elliott, A. Madzvamuse] In this article we propose models and a numerical method for pattern formation on evolving curved surfaces. We formulate reaction-diffusion equations on evolving surfaces using the material transport formula, surface gradients and diffusive conservation laws. The evolution of the surface is defined by a material surface velocity. The numerical method is based on the evolving surface finite element method. The key idea is based on the approximation of Γ by a triangulated surface Γ h consisting of a union of triangles with vertices on Γ. A finite element space of functions is then defined by taking the continuous functions on Γ h which are linear affine on each simplex of the polygonal surface. To demonstrate the capability, flexibility, versatility and generality of our methodology we present results for uniform isotropic growth as well as anisotropic growth of the evolution surfaces and growth coupled to the solution of the reaction-diffusion system. The surface finite element method provides a robust numerical method for solving partial differential systems on continuously evolving domains and surfaces with numerous applications in developmental biology, tumour growth and cell movement and deformation. Springer-Verlag, 2011 Pattern formation nationallicence Evolving surfaces nationallicence Surface finite element method nationallicence Reaction-diffusion systems nationallicence Activator-depleted model nationallicence Barreira R. Escola Superior de Tecnologia do Barreiro/IPS, Rua Américo da Silva Marinho-Lavradio, 2839-001, Barreiro, Portugal aut Elliott C. Mathematics Institute and Centre for Scientific Computing, University of Warwick, CV4 7AL, Coventry, UK aut Madzvamuse A. Department of Mathematics, University of Sussex, Falmer, BN1 9QH, Brighton, UK aut Journal of Mathematical Biology Springer-Verlag 63/6(2011-12-01), 1095-1119 0303-6812 63:6<1095 2011 63 285 https://doi.org/10.1007/s00285-011-0401-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00285-011-0401-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Barreira R. Escola Superior de Tecnologia do Barreiro/IPS, Rua Américo da Silva Marinho-Lavradio, 2839-001, Barreiro, Portugal aut NATIONALLICENCE 700 1- Elliott C. Mathematics Institute and Centre for Scientific Computing, University of Warwick, CV4 7AL, Coventry, UK aut NATIONALLICENCE 700 1- Madzvamuse A. Department of Mathematics, University of Sussex, Falmer, BN1 9QH, Brighton, UK aut NATIONALLICENCE 773 0- Journal of Mathematical Biology Springer-Verlag 63/6(2011-12-01), 1095-1119 0303-6812 63:6<1095 2011 63 285 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer