Abstract:

We chose fourth order Lagrange interpolated function associated with the nodes as trial function, piecewise constant function as test function, and derivative superconvergent points as dual partition nodes so that a new kind of Lagrange fourth order finite volume element method was obtained for solving twopoint boundary value problems. It was proved that the method has optimal H¹ and L² error estimates. The superconvergence of numerical derivatives was discussed. Finally, the numerical experiments show the results of theoretical analysis.

Key words: twopoint boundary value problem, fourth order finite volume element method, derivative superconvergent point, error estimate