| 三次B样条有限元法 |
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| 引用本文： | 秦丹丹,华宏图,张永坡.三次B样条有限元法[J].长春师范学院学报,2011(8):8-10. |
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| 作者姓名： | 秦丹丹 华宏图 张永坡 |
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| 作者单位： | 空军航空大学基础部 |
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| 摘 要： | 由于B样条具有紧凑性及良好的光滑性、明确的表达式等优点,所以用B样条求解微分方程时容易进行系数矩阵的计算,从而提高计算效率。本文利用以上优点构造了三次B样条基函数,并用有限元的思想,求解两点边值问题,通过数值实验计算出:在半H1范数下,三次B样条有限元法具有3阶收敛精度;在L2范数下,三次B样条有限元法具有4阶收敛精度,说明三次B样条有限元法具有最佳L2收敛阶。
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| 关 键 词： | B样条 有限元法 H1收敛阶 L2收敛阶 |
Cubic B-Spline Finite Element Method |
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| QIN Dan-dan,HUA Hong-tu,ZHANG Yong-po.Cubic B-Spline Finite Element Method[J].Journal of Changchun Teachers College,2011(8):8-10. |
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| Authors: | QIN Dan-dan HUA Hong-tu ZHANG Yong-po |
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| Institution: | (Department of Foundation Courses,Aviation University of Air Force,Changchun 130022,China) |
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| Abstract: | Since B-spline has the advantages of compactedness,good smoothness and explicit expression,it is simple to calculate coefficient matrix in the solution of differential equations with B-spline,thus the efficiency of calculation will be improved.Based on above advantages,we construct cubic B-spline basic functions,and solve two-point boundary value problems by finite element thoughts.It is calculated by numerical experiments that cubic B-spline finite element method has third-order convergence precision in H1 semi norm and fourth-order convergence precision in L2 norm.Then it is concluded that cubic B-spline finite element method has optimal L2 convergence order. |
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| Keywords: | B-spline finite element method H1 convergence order L2 convergence order |
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