A conservative characteristic finite volume element method for solution of the advection–diffusion equation

We develop a modified characteristic finite volume element method for two-dimensional advection–diffusion problem in a convex spacial domain, using quasi-uniform triangular discretization and piecewise linear element. This scheme conserves mass globally, and locally on the Lagrangian space–time control volume. We give the optimal order H1-norm and optimal L2-norm error estimates. Finally we present some numerical examples.