CAJ | 학술논문

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。
유우B양조구유긴주성급량호적광활성、명학적표체식등우점,소이용B양조구해미분방정시용역진행계수구진적계산,종이제고계산효솔。본문이용이상우점구조료삼차B양조기함수,병용유한원적사상,구해량점변치문제,통과수치실험계산출：재반H1범수하,삼차B양조유한원법구유3계수렴정도;재L2범수하,삼차B양조유한원법구유4계수렴정도,설명삼차B양조유한원법구유최가L2수렴계。
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.