四阶非线性分数阶反应扩散方程的混合有限元方法  

Mixed finite element method for a nonlinear fourth-order reaction-diffusion problem with fractional derivative

作　　者：覃燕梅[1] QIN Yanmei(School of Mathematics and Information Sciences,Neijiang Normal University,Neijiang,Sichuan 641100,China)

机构地区：[1]内江师范学院数学与信息科学学院,四川内江641100

出　　处：《内江师范学院学报》2023年第10期52-58,共7页Journal of Neijiang Normal University

基　　金：四川省教育厅自然科学基金项目(16ZB0300);2023年度内江市基础研究与应用基础研究项目。

摘　　要：将含参数θ的二阶差分格式与Galerkin有限元法相结合,求解具有时间分数阶导数的四阶非线性反应扩散方程的数值解.在t k-θ(θ∈[0,1/2])时刻,采用θ格式结合分数阶导数的加权移位Gr unwald差分(WSGD)格式对时间离散,在空间上,采用Galerkin有限元方法离散.通过讨论和分析,导出了该方法的无条件稳定性,并给出了先验误差估计,证明了误差结果在时间上可达到二阶精度.To solute the nonlinear fourth-order reaction-diffusion problem with time fractional derivative,some second-order time discrete schemes covering parameterθcombined with Galerkin finite element method are proposed and analyzed.At time t k-θ(θ∈[0,1/2]),some second-orderθschemes combined with weighted and shifted Grunwald difference(WSGD)approximation of fractional derivative are used to discrete the time direction,and the Galerkin finite element method is used to discretize the space direction.Through detailed discussion and analysis,the unconditional stability of the method is derived,and the prior error estimation is given.It is proved that the error results can achieve second-order accuracy in time.

关 键 词：分数阶反应扩散方程 混合有限元 非线性 

分 类 号：O241.82[理学—计算数学]