$hp$-Optimal discontinuous Galerkin methods for linear elliptic problems

Benjamin Stamm, Thomas P. Wihler
2010 Mathematics of Computation  
The aim of this paper is to overcome the well-known lack of poptimality in hp-version discontinuous Galerkin (DG) discretizations for the numerical approximation of linear elliptic problems. For this purpose, we shall present and analyze a class of hp-DG methods that is closely related to other DG schemes, however, combines both p-optimal jump penalty as well as lifting stabilization. We will prove that the resulting error estimates are optimal with respect to both the local element sizes and
more » ... element sizes and polynomial degrees.
doi:10.1090/s0025-5718-10-02335-5 fatcat:pssesiea7bgldcesbtaz5ravji