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Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods, J. Comput. Phys, vol.198, pp.106-130, 2004. ,
Discrete dispersion relation for hp-version finite element approximation at high wave number, SIAM J. Numer. Anal, vol.42, issue.2, p.553575, 2004. ,
Dispersive and dissipative properties of discontinuous Galerkin finite element methods for the secondorder wave equation, Journal of Scientific Computing, vol.27, pp.5-40, 2006. ,
Dispersive behaviour of high order finite element schemes for the one-way wave equation, J. Comput. Phys, vol.259, pp.1-10, 2014. ,
A class of computationally fast first order finite volume solvers: PVM methods, SIAM J. Sci. Comput, vol.34, pp.2173-2196, 2012. ,
Dispersion analysis of compatible Galerkin schemes for the 1d shallow water model, J. Comput. Phys, vol.371, 2018. ,
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Dispersion analysis of compatible Galerkin schemes on quadrilaterals for shallow water model, J. Comput. Phys, vol.387, pp.539-568, 2019. ,
Theory and practice of finite elements, 2004. ,
, Superconvergence of discontinuous Galerkin and local discontinuous Galerkin methods: Eigen-structure analysis based on Fourier approach, vol.235, pp.458-485, 2013.
Insight through theory, Nodal Discontinuous Galerkin Methods. Texts in Applied Mathematics, vol.54, 2008. ,
An analysis of the discontinuous Galerkin method for wave propagation problems, J. Comput. Phys, vol.151, pp.921-946, 1999. ,
Eigensolution analysis of the discontinuous Galerkin method with nonuniform grids, J. Comput. Phys, vol.182, pp.516-545, 2002. ,
, An analysis of the spectrum of the discontinuous Galerkin method, vol.64, pp.1-18, 2013.
, Waves in the Ocean, 1978.
Stability/dispersion analysis of the discontinuous Galerkin linearized shallow-water system, Int. J. Numer. Meth. Fluid, vol.48, pp.325-347, 2005. ,
, Determinants of Sums, vol.21, pp.130-135, 1990.
Dispersion analysis of the spectral element method, Q. J.R. Meteorol. Soc, vol.138, pp.1934-1947, 2012. ,
Spatial eigensolution analysis of discontinuous Galerkin schemes with practical insights for under-resolved computations and implicit LES, Computers & Fluids, vol.169, pp.349-364, 2018. ,
Superconvergence in finite element methods and meshes that are locally symmetric with respect to a point, SIAM J. Numer. Anal, vol.33, issue.2, p.505521, 1996. ,
Dispersion analysis of the continuous and discontinuous Galerkin formulations, Discontinuous Galerkin Methods: Theory, Computation and Applications, vol.11, pp.425-431, 1999. ,
, Finite Difference Schemes and Partial Differential Equations, 2004.
Impact and importance of hyperdiffusion on the spectral element method: A linear dispersion analysis, J. Comput. Phys, vol.375, pp.427-446, 2018. ,
Analysis of spurious oscillation modes for the shallow water and Navier-Stokes equations, Computers and Fluids, vol.11, pp.51-68, 1983. ,
, Numerical resolution of discontinuous Galerkin methods for time dependent wave equations, vol.200, pp.2814-2827, 2011.