- 期刊
B-spline Finite Element Method Applied to Boundary Value Problem and Convergence Rate Analysis
B-spline有限元素法解邊界值問題與收歛速率分析
摘要
本文採用開放均勻B-spline函數做為有限元素的插值函數解邊界值問題，比較B-spline與Lagrange有限元素法的數值解，發現B-spline數值解的誤差的L2與能量模收歛速率比Lagrange數值解快，而且B-spline的結果是連續的；反之，Lagrange的結果不是連續的，因此，當需要高精密度的數值解時，B-spline有限元素法的計算所需的時間較Lagrange有限元素法來的。
關鍵字
無資料並列摘要
This paper adopts the open uniform B-spline functions as finite element interpolation functions to solve the boundary value problem. It compares the numerical solutions of the B-spline finite element method with those of the Lagrange finite element method. The convergence rate of the B-spline solutions is better than that of the Lagrange method, and the results of the B-spline were continuous, whereas those of the Lagrange method were discontinuous. Consequently, when high accuracy numerical solutions are required, the B-spline finite element methods are less time-consuming than the Lagrange method.
延伸閱讀
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