WEDNESDAY, January 29, 2003
Time: 2:00 - 3:00 PM
BAL 340

Dr. Fang Hu
Department of Mathematics & Statistics, Old Dominion University

The discontinuous Galerkin method is a finite element method that allows discontinuities at element interfaces. In most Fourier analyses of discontinuous Galerkin schemes for hyperbolic systems, a spatial wavenumber is specified and the corresponding temporal frequency is computed as an eigenvalue of the semi-discrete equations. The relation of the two yields the numerical dispersion relation. In the present study, we reverse this process by specifying the temporal frequency and compute the corresponding spatial wavenumber. There are two advantages in this approach. First, due to compactness of the scheme, the eigenvalue problem is simplified and reduced to a quadratic algebraic equation, for any given order of the basis functions. This allows the numerical dispersion relation be solved analytically, which will subsequently be shown to be super-accurate for discontinuous Galerkin schemes. Second, the wave reflection and transmission at an interface of grid stretching, or other forms of grid variation, can be analyzed analytically using the eigensolutions so formed. Expressions of numerical reflection and transmission coefficients will be derived and analyzed for various flux formulas. All the findings of the study will be illustrated through numerical examples.