A Uniform-Consistency Barrier on Finite-Difference Schemes of Positive Type for Convection-Diffusion Equations | Zendy

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A Uniform-Consistency Barrier on Finite-Difference Schemes of Positive Type for Convection-Diffusion Equations

Author(s) -

Hao Lu

Publication year - 1995

Publication title -

siam journal on scientific computing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.674

H-Index - 147

eISSN - 1095-7197

pISSN - 1064-8275

DOI - 10.1137/0916011

Subject(s) - mathematics , nabla symbol , type (biology) , convection–diffusion equation , consistency (knowledge bases) , finite difference method , diffusion , finite difference , convection , mathematical analysis , scheme (mathematics) , geometry , physics , omega , thermodynamics , quantum mechanics , ecology , biology

In this note the author shows a uniform-consistency barrier on finite-difference schemes of positive type for convection-diffusion equations; i.e., any difference scheme of positive type cannot approximate $Lu = - \varepsilon \Delta u + \vec f \cdot \nabla u + gu$ to $O(h^\alpha )$$(\alpha > 1)$ accuracy uniformly in $\varepsilon $.

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