Extended Fisher-Kolmogorov方程的间断有限元分析  

Discontinuous Galerkin Finite Element Analysis of for the Extended Fisher-Kolmogorov Equation

作　　者：杨晓侠 张厚超 Yang Xiaoxia;Zhang Houchao(School of Mathematics and Statistics,Pingdingshan University,Henan Pingdingshan 467000)

机构地区：[1]平顶山学院数学与统计学院,河南平顶山467000

出　　处：《数学物理学报（A辑）》2021年第6期1880-1896,共17页Acta Mathematica Scientia

基　　金：国家自然科学基金(11271340,11671369);2020年度河南省高等学校重点科研项目(20A110030,20B110013);平顶山学院高层次人才启动基金(PXY-BSQD-2019001)。

摘　　要：利用Wilson元研究了Extended Fisher-Kolmogorov(EFK)方程的间断有限元逼近格式.在不需要后处理技术的前提下,通过对非线性项采用新的分裂技术,分别得到了半离散和线性化欧拉全离散格式下原始变量u和中间变量v=-△u的O(h^(2))和O(h^(2)+τ)阶的收敛性结果,正好比通常的关于Wilson元的误差估计高出一阶.这里,h,τ表示空间剖分参数和时间步长.The discontinuous Galerkin finite element approximation schemes for the Extended Fisher-Kolmogorov(EFK)equation are studied by using the Wilson element.Without using the technique of postprocessing technique,the convergence results with order O(h^(2))/O(h^(2)+τ)for the primitive solution u and intermediate variable v=-△u are obtained for the semidiscrete and linearized Euler fully discrete approximation schemes respectively through a new splitting technique for the nonlinear terms.The above results are just one order higher than the usual error estimates of the Wilson element.Here,h andτare parameters of the subdivision in space and time step,respectively.

关 键 词：EFK方程 间断有限元 WILSON元 半离散和全离散格式 收敛性 

分 类 号：O242.21[理学—计算数学]