Multilevel Preconditioners for the Interior Penalty Discontinuous Galerkin Method II - Quantitative Studies

Abstract

This paper is concerned with preconditioners for interior penalty discontinuous Galerkin discretizations of second-order elliptic boundary value problems. We extend earlier related results in [7] in the following sense. Several concrete realizations of splitting the nonconforming trial spaces into a conforming and (remaining) nonconforming part are identified and shown to give rise to uniformly bounded condition numbers. These asymptotic results are complemented by numerical tests that shed some light on their respective quantitative behavior.