Very high-order finite volume scheme for 1D convection diffusion problem: the implicit case - Machado, Gaspar J. (2012)
We present a fourth-order in space, second-order in time finite volume scheme for transient convection diffusion problem based on the Polynomial Reconstruction Operator and a Crank-Nicholson method. A detailed description of the scheme is provided and we perform numerical tests to highlight the performance of the method in comparison with the classical Patankar method.