u
,∇u)=f, is to take the average onto the same mesh of the two equations of the mixed form, the conservation law div p=f and the constitutive law p=ϕ(u,∇u). In this paper, we perform the numerical analysis of two Keller-like box-schemes for the one-dimensional convection-diffusion equation cu x −ɛu xx =f. In the first one, introduced by B. Courbet in [9,10], the numerical average of the diffusive flux is upwinded along the sign of the velocity, giving a first order accurate scheme. The second one is fourth order accurate. It is based onto the Euler-MacLaurin quadrature formula for the average of the diffusive flux. We emphasize in each case the link with the SUPG finite element method.
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Received June 7, 2001; revised October 2, 2001
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Croisille, JP. Keller's Box-Scheme for the One-Dimensional Stationary Convection-Diffusion Equation. Computing 68, 37–63 (2002). https://doi.org/10.1007/s006070200002
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DOI: https://doi.org/10.1007/s006070200002