Superconvergence of a discontinuous finite element method for a nonlinear ordinary differential equation

Abstract In this paper, n -degree discontinuous finite element method with interpolated coefficients for an initial value problem of nonlinear ordinary differential equation is introduced and analyzed. By using the finite element projection for an auxiliary linear problem as comparison function, an optimal superconvergence u - U = O ( h n + 2 ) , n ⩾ 2 , at ( n  + 1)-order characteristic points in each element respectively is proved. Finally the theoretic results are tested by a numerical example.