非线性时间分布阶反应扩散耦合系统的二阶θ格式的有限元方法

A Finite Element Method with Second-order θ Scheme for Nonlinear Time Distributed-order Coupled Sub-diffusion System

构造了一种基于二阶θ格式的有限元(FEM)算法,用于求解非线性时间分布阶反应扩散耦合系统。使用二阶θ格式结合数值求积公式逼近时间分布阶导数,进一步形成有限元全离散格式。证明了格式的稳定性以及两个函数u和v的最优误差估计结果。最后通过数值算例验证了格式的有效性。

A finite element method(FEM)based on second-orderθscheme is presented to solve a nonlinear time distributed-order coupled sub-diffusion system.The second-orderθscheme combined with the numerical quadrature formula is used for the time distributed-order dericative.Then the finite element fully discrete scheme is obtained.The stability and error estimates for two functions u and v are derived.Some numerical examples are provided to indicate the efficiency of our schemes.