An Analysis of the Dissipation and Dispersion Errors of the PNPM Schemes
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We examine the dispersion and dissipation properties of the PNPM schemes for linear wave propagation problems. PNPM scheme are based on PN discontinuous Galerkin base approximations augmented with a cell centered polynomial least-squares reconstruction from degree N up to the design polynomial degree M. This methodology can be seen as a generalized discretization framework, as cell centered high order finite volume schemes (N=0) and discontinuous Galerkin schemes (N=M) are included as special cases.
We show that with respect to the dispersion error, the pure discontinuous Galerkin variant gives typically the best accuracy for a defined number of points per wavelength. Regarding the dissipation behavior, combinations of N and M exist that result in slightly lower errors for a given resolution. An investigation of the influence of the stencil size on the accuracy of the scheme shows that the errors are smaller the smaller the stencil size for the reconstruction.
KeywordsDispersion Dissipation Reconstructed discontinuous Galerkin PNPM schemes Wave propagation
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