Publications [#372382] of Di Fang

Papers Published

1. Fang, D; Jin, S; Markowich, P; Perthame, B, Implicit and Semi-implicit Numerical Schemes for the Gradient Flow of the Formation of Biological Transport Networks, Smai Journal of Computational Mathematics, vol. 5 (January, 2019), pp. 229-249 [doi]
   (last updated on 2026/01/15)

   Abstract:
   Implicit and semi-implicit time discretizations are developed for the Cai–Hu model describing the formation of biological transport networks. The model couples a nonlinear elliptic equation for the pressure with a nonlinear reaction-diffusion equation for the network conductance vector. Numerical challenges include the non-linearity and the stiffness, thus an explicit discretization puts severe constraints on the time step. We propose an implicit and a semi-implicit discretizations, which decays the energy unconditionally or under a condition independent of the mesh size respectively, as will be proven in 1D and verified numerically in 2D.