Short Note: On the connection between the spectral volume and the spectral difference method
Journal of Computational Physics
Spatial and temporal competition as a two dimensional kinetic Voronoi diagram
Computer-Aided Design
Short Note: A stability analysis for the spectral volume method on tetrahedral grids
Journal of Computational Physics
A Study of Viscous Flux Formulations for a p-Multigrid Spectral Volume Navier Stokes Solver
Journal of Scientific Computing
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In this paper, we present several systematic techniques, based on the Voronoi diagram and its variants, to partition a one- and two-dimensional simplex. The Fekete points are used as input to generate the Voronoi diagram, as they concentrate near the edges and are almost optimal for polynomial interpolation in a simplex.Spectral (finite) volume reconstructions on the resultant partitions have small Lebesgue constants. When using the Dubiner basis, the reconstruction matrix is well conditioned. Moreover, the total number of edges of the partitions (the total work when being used in spectral volume methods) is shown to be at most twice the minimum number of edges of all partitions for reconstructions of the same order accuracy. These suggest that the obtained partitions are well suited for spectral volume methods and other numerical methods which rely on reconstructions from cell averages.