A Galerkin Method for the Convection—Diffusion Equation Using Asymmetric Weighting Functionsby James A. Cardle, Univ of Nevada, Las Vegas, Las Vegas, United States,
Abstract: A variation of the Petrov-Galerkin method of solution of a partial differential equation is presented in which the weight function applied to the time derivative term of a one-dimensional convection-diffusion equation is different from the weight function applied to the spatial derivatives. Although the no damping case is the most accurate, spurious oscillations can result in the presence of steep fronts in strongly convective flows. If damping is added, the approach described in this paper allows for different damping components α and β respectively on the time derivative and convective terms which has advantages over the usual Petrov-Gelerkin technique.
Subject Headings: Damping | Groundwater flow | Diffusion | Water flow | Hydrologic models | Heat flow | Differential equations | Advection
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