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Dispersion analysis of the continuous and discontinuous Galerkin formulations. (English) Zbl 0946.65084

Cockburn, Bernardo (ed.) et al., Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24-26, 1999. Berlin: Springer. Lect. Notes Comput. Sci. Eng. 11, 425-431 (2000).
Summary: The dispersion relation of the semidiscrete continuous and discontinuous Galerkin formulations are analyzed for the linear advection equation. In the context of an spectral/\(hp\) element discretization on an equispaced mesh the problem can be reduced to a \(P\times P\) eigenvalue problem where \(P\) is the polynomial order. The analytical dispersion relationships for polynomial order up to \(P= 3\) and the numerical values for \(P=10\) are presented demonstrating similar dispersion properties but show that the discontinuous scheme is more diffusive.
For the entire collection see [Zbl 0935.00043].

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems
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