【摘要】 构造求解两点边值问题的一种Hermite型五次元高精度有限体积法,其中试探函数空间取Hermite型五次有限元空间,与Hermite型三次元相同,未引入更高阶导数作为插值条件,检验函数空间取分段线性函数空间,这样构造的格式求解精度更高.并分别给出了解的H1模和L2模的最优收敛阶估计,L2模收敛阶比H1模收敛阶高一阶.数值实验结果验证了方法的有效性和正确性.更多还原

【Abstract】 We constructed a finite volume scheme of fifth-order Hermite type with high accuracy for two-point boundary value problems,choosing trial and test spaces as the fifth-order finite element space of Hermite type and the piecewise linear function space respectively.We didn’t use higher derivatives as interpolation conditions,which is the same as the third-order finite element of Hermite type,but the scheme obtained had higher accuracy.The optimal convergence rates in H1 and L2 norms are proved,and the convergence order in L2 norm is one order higher than that in H1 norm.The numerical examples confirm the theoretical results.更多还原