Abstract A theoretical error analysis using standard Sobolev space energy arguments is furnished for a class of discontinuous Galerkin (DG) schemes that are modified versions of one of those introduced by van Leer and Nomura. These schemes, which use discontinuous piecewise polynomials of degree q , are applied to a family of one-dimensional elliptic boundary value problems. The modifications to the original method include definition of a recovery flux function via a symmetric L 2 -projection and the addition of a penalty or stabilization term. The method is found to have a convergence rate of O ( h q ) for the approximation of the first derivative and O ( h q +1 ) for the solution. Computational results for the original and modified DG recovery schemes are provided contrasting them as far as complexity and cost. Numerical examples are given which exhibit sub-optimal convergence rates when the stabilization terms are omitted.