A fractional step θ-method for convection–diffusion problems

• Published in: Journal of mathematical analysis and applications Vol. 333; no. 1; pp. 204 - 218
• Main Authors: Chrispell, J.C., Ervin, V.J., Jenkins, E.W.
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.09.2007; Elsevier
• Subjects: Calculus of variations and optimal control; Convection–diffusion; Exact sciences and technology; Mathematical analysis; Mathematics; Sciences and techniques of general use; Splitting method; θ-method; Splitting method; Convection–diffusion; θ-method; Second order; Error estimation; Fractional step method; Step method; 0-method; Convection-diffusion; Convection diffusion equation; Implementation; Galerkin-Petrov method; Splitting; Convection equation; Numerical computation; Mathematical analysis; A priori estimation; Diffusion equation; Galerkin method; Application
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2006.11.059

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.