Perugia, IlariaSchotzau, Dominik2007-08-162007-08-162001-06https://hdl.handle.net/11299/3653We present an $hp$-analysis of the local discontinuous Galerkin method for diffusion problems, considering unstructured meshes with hanging nodes and two- and three-dimensional domains. Our estimates are optimal in the meshsize $h$ and slightly suboptimal in the polynomial approximation order $p$.