A fractional step θ-method for convection–diffusion problems

In this article, we analyze the fractional step θ-method for the time-dependent convection–diffusion equation. In our implementation, we completely separate the convection operator from the diffusion operator, and stabilize the convective problem using a Streamline Upwinded Petrov–Galerkin (SUPG) method. We establish a priori error estimates and show that the optimal value of θ yields a scheme that is second-order in time. Numerical computations are presented which demonstrate the method and support the theoretical results.