title: A new linearized Crank-Nicolson mixed element scheme for the extended Fisher-Kolmogorov equation.
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 (L²(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 L² and H¹-norm for both the scalar unknown u and the diffusion term w = -Δu and a priori error estimates in (L²)²-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes.
authors.affiliation: School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China.
authors.forename: Jinfeng
authors.initials: J
authors.lastname: Wang
authors.forename: Hong
authors.initials: H
authors.lastname: Li
authors.forename: Siriguleng
authors.initials: S
authors.lastname: He
authors.forename: Wei
authors.initials: W
authors.lastname: Gao
authors.forename: Yang
authors.initials: Y
authors.lastname: Liu
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D020342:Finite Element Analysis; D016014:Linear Models; D009716:Numerical Analysis, Computer-Assisted