Abstract:

In this paper, a new kind of Lagrangian quadratic finite volume element method based on optimal stress points is presented for solving two\|point boundary value problems. In general,  trial and test spaces are chosen as the Lagrangian quadratic finite element space and the piecewise constant function space respectively. It is proved that the method has optimal H¹ and L² error estimates. The superconvergence of numerical derivatives at optimal stress points is discussed. Finally, the numerical experiments show the results of theoretical analysis.

Key words: twopoint boundary value problem, quadratic finite volume element method, optimal stress point, error estimate