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| 具有变系数四阶抛物方程的B样条有限元法 | |
| 引用本文： | 秦丹丹,唐鑫鑫,黄文竹.具有变系数四阶抛物方程的B样条有限元法[J].吉林大学学报(理学版),2020,58(5):1100-1106. |
| 作者姓名： | 秦丹丹 唐鑫鑫 黄文竹 |
| 作者单位： | 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 |
| 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+h4). 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. |
| 关 键 词： | 变系数 四阶抛物方程 B样条 有限元法 |
| 收稿时间： | 2020-02-27 |
B-Spline Finite Element Method for Fourth Order Parabolic Equations with Variable Coefficient |
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| QIN Dandan,TANG Xinxin,HUANG Wenzhu.B-Spline Finite Element Method for Fourth Order Parabolic Equations with Variable Coefficient[J].Journal of Jilin University: Sci Ed,2020,58(5):1100-1106. | |
| Authors: | QIN Dandan TANG Xinxin HUANG Wenzhu |
| Institution: | 1. Department of Fundation, Aviation University of Air Force, Changchun 130022, China; 2. College of Mathematics, Jilin University, Changchun 130012, China; 3. School of Biology and Engineering, Guizhou Medical University, Guiyang 550025, China |
| Abstract: | 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+h4). A numerical experiment verified the effectiveness of theoretical analysis results and the B-spline finite element method. |
| Keywords: | variable coefficient fourth order parabolic equation B-spline finite element method |
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