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Article
Optimal Upstream Collocation Solution of the One-Dimensional Steady-State Convection-Diffusion Equation
International Journal of Applied Mathematics and Computer Science
  • Stephen H. Brill, Boise State University
Document Type
Article
Publication Date
1-1-2002
Disciplines
Abstract
We give herein analytical formulas for the solution of the Hermite collocation discretization of the unforced steady-state convection-diffusion equation in one spatial dimension and with constant coefficients, defined on a uniform mesh, with Dirichlet boundary conditions. The accuracy of the method is advanced by employing "upstream weighting" of the convective term in an optimal way, avoiding both "smearing" and unwanted oscillations, particularly for large Péclet numbers. Computational examples illustrate the efficacy of using optimal upstream weighting.
Citation Information
Stephen H. Brill. "Optimal Upstream Collocation Solution of the One-Dimensional Steady-State Convection-Diffusion Equation" International Journal of Applied Mathematics and Computer Science (2002)
Available at: http://works.bepress.com/stephen_brill/8/