Journal of Computational Physics
A conservative staggered-grid Chebyshev multidomain method for compressible flows
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Spectral difference method for unstructured grids I: basic formulation
Journal of Computational Physics
Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations
Journal of Scientific Computing
On the Stability and Accuracy of the Spectral Difference Method
Journal of Scientific Computing
Spectral difference method for compressible flow on unstructured grids with mixed elements
Journal of Computational Physics
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
A New Class of High-Order Energy Stable Flux Reconstruction Schemes
Journal of Scientific Computing
Insights from von Neumann analysis of high-order flux reconstruction schemes
Journal of Computational Physics
Journal of Computational Physics
On the Non-linear Stability of Flux Reconstruction Schemes
Journal of Scientific Computing
A New Class of High-Order Energy Stable Flux Reconstruction Schemes for Triangular Elements
Journal of Scientific Computing
An optimized spectral difference scheme for CAA problems
Journal of Computational Physics
Journal of Scientific Computing
Energy stable flux reconstruction schemes for advection-diffusion problems on triangles
Journal of Computational Physics
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While second order methods for computational simulations of fluid flow provide the basis of widely used commercial software, there is a need for higher order methods for more accurate simulations of turbulent and vortex dominated flows. The discontinuous Galerkin (DG) method is the subject of much current research toward this goal. The spectral difference (SD) method has recently emerged as a promising alternative which can reduce the computational costs of higher order simulations. There remains some questions, however, about the stability of the SD method. This paper presents a proof that for the case of one dimensional linear advection the SD method is stable for all orders of accuracy in a norm of Sobolev type, provided that the interior fluxes collocation points are placed at the zeros of the corresponding Legendre polynomial.