Analysis of a family of discontinuous Galerkin methods for elliptic problems: the one dimensional case (Q706221)

This paper deals with the properties of discontinuous Galerkin methods for elliptic problems in one spatial dimension. The analysis is based on a splitting of the discrete space into a direct sun of continuous piecewise polynomials and a space representing the discontinuous part of the functions also satisfying a special orthogonality relation. The authors prove stability results and \(L^2\) error estimates. Finally, some remarks on the elementwise conservative nature of the discontinuous Galerkin method are presented.