关键词: 两点边值问题, 五次有限体积法, 超收敛, 误差估计

Abstract:

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 a piecewise 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.

Key words: twopoint boundary value problem, fifthorder finite volume element method, superconvergence, error estimate