Chapter

Discontinuous Galerkin methods (DCGMs), with V. Dolejší

Klaus Böhmer

in Numerical Methods for Nonlinear Elliptic Differential Equations

Published in print October 2010 | ISBN: 9780199577040
Published online January 2011 | e-ISBN: 9780191595172 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199577040.003.0007

Series: Numerical Mathematics and Scientific Computation

Discontinuous Galerkin methods (DCGMs), with V. Dolejší

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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.

Keywords: DCGMs; boundary conditions; discontinuity of FEs; additional penalty terms; hp-variants; numerical experiences; steady compressible Navier-Stokes equations

Chapter.  19938 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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