Finite-element approximation of a nonlinear degenerate parabolic system describing bacterial pattern formation (Q1613198)

A finite element discretization is applied to a system of nonlinear degenerated parabolic partial differential equations in one and two space dimensions. Stability bounds of the approximation are devised and a proof for convergence and existence of the nonlinear system is given. The system of governing equations is applied to model bacterial pattern formation in a thin film of nutrient. Numerical simulations in one and two spatial dimensions using an iterative procedure show the numerical convergence of the scheme and illustrate different types of bacterial pattern formation.