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Necessary convergence conditions for upwind schemes in the two- dimensional case. (English) Zbl 0578.65098
Generalizing an approach due to J. J. H. Miller, the two-dimensional elliptic diffusion-convection equation with constant coefficients is considered and necessary conditions for the convergence (uniform in the small diffusion coefficient) of upwind schemes (defined on a 9-point stencil) are derived. Seven specific approximations are investigated. Partly negative answers are obtained, partly a unique determination of the free parameters results.
Reviewer: G.Stoyan

MSC:
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
35B25 Singular perturbations in context of PDEs
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