Adaptive moving mesh computations for reaction–diffusion systems

In this paper we describe an adaptive moving mesh technique and its application to reaction–diffusion models from chemistry. The method is based on a coordinate transformation between physical and computational coordinates. The transformation can be viewed as a solution of adaptive mesh partial differential equations (PDEs) which is derived from the minimization of a mesh-energy integral. For an efficient implementation we have used an approach in which the numerical solution of the physical PDEs and the adaptive PDEs are decoupled. Further, to avoid solving large nonlinear systems, a second-order implicit–explicit time-integration method in combination with the iterative method Bi-CGSTAB is applied in the method-of-lines procedure. Numerical examples are given in one and two space dimensions.