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 method for linear and non-linear convection-diffusion problems in one dimension. For linear problems, the stability proof relies on compactness arguments developed by Grigorieff. However, Grigorieff's ideas have had to be extended to account for non-compact schemes. The analysis establishes second-order convergence of both the approximate solution and its gradient. This is despite the fact that the scheme is only first-order consistent. The analysis of the linear problem is taken over to non-linear problems via the theory of Lopez-Marcos and Sanz-Serna. Numerical experiments are provided which back up the analysis.