中文摘要：

构造基于Lobatto-Gauss结构的有限体积法,试探空间取六次Lobatto多项式零点为插值节点的Lagrange型五次有限元空间,检验函数空间取五阶Gauss多项式零点为插值节点的分片常数空间.证明了这种格式的稳定性和收敛性以及在应力佳点导数的超收敛性,并通过数值实验验证了理论分析结果.结果表明,所给方法具有最优的H1模和L2模误差估计.

英文摘要：

A one-dimension fifth-order finite volume method based on the Lobatto-Gauss constructure was designed,with its trial function being the fifth order Lagrange interpolated function,and the test function space being apiecewise constant space.The stability and convergence of the scheme was proved.The H1 and L2 error estimates were proved to be optimal.We discussed the superconvergence of numerical derivatives at optimal stress points.And the numerical experiments show the results of theoretical analysis.