An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation
Mathematics of Computation
A note on the convergence of the discontinuous Galerkin method for a scalar hyperbolic equation
SIAM Journal on Numerical Analysis
An analysis of the discontinuous Galerkin method for wave propagation problems
Journal of Computational Physics
Dispersion Analysis for Discontinuous Spectral Element Methods
Journal of Scientific Computing
Nodal high-order methods on unstructured grids
Journal of Computational Physics
Journal of Computational Physics
Discrete Dispersion Relation for hp-Version Finite Element Approximation at High Wave Number
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
Journal of Computational Physics
Journal of Scientific Computing
Journal of Scientific Computing
Journal of Scientific Computing
Dispersive and Dissipative Behavior of the Spectral Element Method
SIAM Journal on Numerical Analysis
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The dispersion and dissipation properties of numerical methods are very important in wave simulations. In this paper, such properties are analyzed for Runge-Kutta discontinuous Galerkin methods and Lax-Wendroff discontinuous Galerkin methods when solving the linear advection equation. With the standard analysis, the asymptotic formulations are derived analytically for the discrete dispersion relation in the limit of K=kh驴0 (k is the wavenumber and h is the meshsize) as a function of the CFL number, and the results are compared quantitatively between these two fully discrete numerical methods. For Lax-Wendroff discontinuous Galerkin methods, we further introduce an alternative approach which is advantageous in dispersion analysis when the methods are of arbitrary order of accuracy. Based on the analytical formulations of the dispersion and dissipation errors, we also investigate the role of the spatial and temporal discretizations in the dispersion analysis. Numerical experiments are presented to validate some of the theoretical findings. This work provides the first analysis for Lax-Wendroff discontinuous Galerkin methods.