Analysis of spectral volume methods for 1D linear scalar hyperbolic equations (Q2063216)

The authors study the \(L^2\)-norm stability, convergence and superconvergence properties of two classes of SV (spectral volume) methods for linear hyperbolic conservation laws in the one-dimensional setting. The first class is constructed basing on the Gauss-Legendre points (LSV) and the other is based on the right-Radau points (RRSV). Moreover, it is shown that for constant-coefficient equations, the RRSV method is identical to the upwind discontinuous Galerkin (DG) method. Some numerical tests are presented to support the theoretical results.