Second-order implicit–explicit scheme for the Gray–Scott model

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摘要

A second-order scheme for the Gray–Scott (GS) model used to describe the pattern formation is studied. The linear part of the GS equation for the time derivative and the viscous terms is discretized implicitly, while the other (or nonlinear) part of the GS equation explicitly. Galerkin finite element approximation methods are presented and analyzed, as well as methods for solving the resulting system of equations. The optimal L2-norm error estimates are derived. Numerical experiments are presented.

论文关键词：65M60,65M12,65L06,Finite element method,Gray–Scott model,Implicit–explicit scheme,Reaction–diffusion

论文评审过程：Received 7 August 2006, Revised 27 January 2007, Available online 20 February 2007.

论文官网地址：https://doi.org/10.1016/j.cam.2007.01.038