| Affiliation: | School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, Minnesota 55455 ; School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, Minnesota 55455 ; School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, Minnesota 55455 ; Seminar of Applied Mathematics, ETHZ, 8092 Zürich, Switzerland |
| Abstract: | We study the convergence properties of the  -version of the local discontinuous Galerkin finite element method for convection-diffusion problems; we consider a model problem in a one-dimensional space domain. We allow arbitrary meshes and polynomial degree distributions and obtain upper bounds for the energy norm of the error which are explicit in the mesh-width  , in the polynomial degree  , and in the regularity of the exact solution. We identify a special numerical flux for which the estimates are optimal in both  and  . The theoretical results are confirmed in a series of numerical examples. |
