Very high-order finite volume scheme for 1D convection diffusion problem: the implicit case

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.
FEDER Funds through Programa Operacional Factores de Competitividade — COMPETE
Fundação para a Ciência e a Tecnologia (FCT) - Projeto PEst-C/MAT/UI0013/2011.