Abstract:

A fifth-order finite volume element scheme was constructed for twopoint boundary value problems, in which trial and test spaces were chosen as the fifth-order finite element space and the piecewise quadratic function space respectively. The optimal convergence rates in H¹ and L² norm were proved, and the superconvergence of the scheme was obtained. The numerical examples confirm the theoretical results.

Key words: finite volume element method, trial function spaces, dual partition, test function spaces