Time integration of the non-linear Galerkin method

e-mail: bosco{at}mac.cie.uva.es, frutos@mac.cie.uva.es Numerical tests are presented that, for the Kuramoto-Sivashinskyand a reaction-diffusion equation, compare the non-linear Galerkinmethod with standard pseudospectral and pure spectral Galerkindiscretizations. The results show that, for these problems,the non-linear Galerkin method is not competitive with eitherpure spectral Galerkin or pseudospectral discretizations.     

Analysis of a supraconvergent cell vertex finite-volume method for one-dimensional convection-diffusion problems

In this paper we analyze a cell vertex finite-volume methodfor linear and non-linear convection-diffusion problems in onedimension. For linear problems, the stability proof relies oncompactness arguments developed by Grigorieff. However, Grigorieff'sideas have had to be extended to account for non-compact schemes.The analysis establishes second-order convergence of both theapproximate solution and its gradient This is despite the factthat the scheme is only first-order consistent. The analysisof the linear problem is taken over to non-linear problems viathe theory of Lpez-Marcos and Sanz-Serna. Numerical experimentsare provided which back up the analysis.