具有变系数四阶抛物方程的B样条有限元法  

B-Spline Finite Element Method for Fourth Order Parabolic Equations with Variable Coefficient

作　　者：秦丹丹[1,2] 唐鑫鑫 黄文竹 QIN Dandan;TANG Xinxin;HUANG Wenzhu(Department of Fundation,Aviation University of Air Force,Changchun 130022,China;College of Mathematics,Jilin University,Changchun 130012,China;School of Biology and Engineering,Guizhou Medical University,Guiyang 550025,China)

机构地区：[1]空军航空大学基础部,长春130022 [2]吉林大学数学学院,长春130012 [3]贵州医科大学生物与工程学院,贵阳550025

出　　处：《吉林大学学报（理学版）》2020年第5期1100-1106,共7页Journal of Jilin University:Science Edition

基　　金：贵州省卫健委科技基金(批准号:gzwjkj2019-1-050).

摘　　要：用三次B样条有限元法求解一类四阶主项带有变系数的抛物方程,证明半离散格式解的有界性与收敛性.关于时间变量的离散,通过构造向后Euler格式,得到全离散格式解的收敛阶为O(Δt+h^4).数值算例验证了理论分析结果及B样条有限元法的有效性.We used the cubic B-spline finite element method to solve a class of fourth order parabolic equations with variable coefficient,and proved the boundness and convergence of the solution of the semi-discrete scheme.For the discretization of time variable,the backward Euler scheme was constructed,and the convergence order of the solution of the fully discrete scheme was O(Δt+h^4).A numerical experiment verified the effectiveness of theoretical analysis results and the B-spline finite element method.

关 键 词：变系数 四阶抛物方程 B样条 有限元法 

分 类 号：O241.82[理学—计算数学]