An analysis of and a comparison between the discontinuous Galerkin and the spectral finite volume methods

The discontinuous Galerkin method has been developed and applied extensively to solve hyperbolic conservation laws in recent years. More recently Wang et al. developed a class of discontinuous Petrov–Galerkin method, termed spectral (finite) volume method J. Comput. Phys. 78 (2002) 210; J. Comput. Phys. 179 (2002) 665; J. Sci. Comput. 20 (2004) 137]. In this paper we perform a Fourier type analysis on both methods when solving linear one-dimensional conservation laws. A comparison between the two methods is given in terms of accuracy, stability, and convergence. Numerical experiments are performed to validate this analysis and comparison.