Abstract
Chapter 7 presents with V. Dolejší presents discontinuous Galerkin methods (DCGMs): violated boundary conditions and continuity of the piecewise polynomials are compensated by additional penalty terms in the discrete weak form. This chapter restricts them to linear and quasilinear equations and systems of order 2. hp-variants of DCGMs and numerical experience with the steady compressible Navier-Stokes equations are added. The proof of stability, nearly identical to Chapter 4 based upon the anticrime transformation, is omitted. The relations between the strong and weak forms yield consistency.
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