L2-estimates for the DG IIPG-0 scheme

• ID: 2649, RIV: 10104784
• ISSN: 0749-159X, ISBN: not specified
• source: Numerical Methods for Partial Differential Equations
• keywords: discontinuous Galerkin method; interior penalty
• authors: Oto Havle, Blanca Ayuso de Dios, Franco Brezzi, Donatella Marini
• authors from KNM: not assigned

Abstract

We discuss the optimality in L2 of a variant of the Incomplete Discontinuous Galerkin Interior Penalty method (IIPG) for second order linear elliptic problems.We prove optimal estimate, in two and three dimensions, for the lowest order case under suitable regularity assumptions on the data and on the mesh. We also provide numerical evidence, in one dimension, of the necessity of the regularity assumptions.