C-Bézier和H-Bézier基函数在热传导问题求解中的应用  

Application of C-Bézier and H-Bézier Basis in Solving Heat Conduction Problems

作　　者：孙兰银 苏芳明 SUN Lanyin;SU Fangming(College of Mathematics and Statistics,Xinyang Normal University,Xinyang 464000,China)

机构地区：[1]信阳师范学院数学与统计学院,河南信阳464000

出　　处：《信阳师范学院学报（自然科学版）》2022年第3期358-363,共6页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11801490);河南省高校科技创新人才支持计划项目(22HASTIT021);河南省重点研发与推广专项(科技攻关)项目(212102210394);信阳师范学院研究生科研创新基金项目(2021KYJJ48)。

摘　　要：运用C-Bézier和H-Bézier基函数构造有限元方法中的试探函数和测试函数空间,并分析了误差。通过数值算例,数值解的误差精度较Lagrange基函数提升了1到3个数量级,说明这两类基函数在模拟特定类型的热传导问题时具有更好的逼近效果。C-Bézier and H-Bézier basis functions are applied to the space of trial function and test function in the finite element method and the errors are analyzed.By means of numerical examples,the error accuracy of numerical solution is improved by one to three orders of magnitude compared with Lagrange basis function,it is shown that these two kinds of basis functions have better approximations in simulating specific heat conduction problems.

关 键 词：热传导方程 有限元方法 C-Bézier基函数 H-Bézier基函数 

分 类 号：O242.1[理学—计算数学]