A New Linearized Crank-Nicolson Mixed Element Scheme for the Extended Fisher-Kolmogorov Equation. (22nd June 2013) - Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei; Liu, Yang
Abstract : We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇ u belongs to the weaker ( L 2 ( Ω ) ) 2 space taking the place of the classical H ( div ; Ω ) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L 2 and H 1 -norm for both the scalar unknown u and the diffusion term w = − Δ u and a priori error estimates in ( L 2 ) 2 -norm for its gradient χ = ∇ u for both semi-discrete and fully discrete schemes.