A New Linearized Crank-Nicolson Mixed Element Scheme for the Extended Fisher-Kolmogorov Equation

作者：Wang, Jinfeng; Li, Hong^*; He, Siriguleng; Gao, Wei; Liu, Yang

来源：The Scientific World Journal, 2013, 2013: 756281.

DOI：10.1155/2013/756281

• CAHN-HILLIARD EQUATION
• ACCURACY ANALYSIS
• GALERKIN METHOD
• CONVERGENCE

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 del u belongs to the weaker (L-2 (Omega))(2) space taking the place of the classical H(div; Omega) 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 = -del u and a priori error estimates in (L-2)(2)-norm for its gradient chi = del u for both semi-discrete and fully discrete schemes.

• 出版日期2013
• 单位内蒙古大学