Geodesic
Unconditionally stable schemes for convection-diffusion problems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2013), pp. 3-15

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Convection-diffusion problems are basic ones in continuum mechanics. The main features of these problems are connected with the fact that their operators may have an indefinite sign. In this paper we study stability of difference schemes with weights for convection-diffusion problems where the convective transport operator may have various forms. We present unconditionally stable schemes for non-stationary convection-diffusion equations based on the use of new variables. Similar schemes are also used for parabolic equations where the operator represents the sum of diffusion operators.
Mots-clés : convection-diffusion equations
Keywords: finite difference schemes, stability of difference schemes. 
@article{IVM_2013_3_a0,
     author = {N. M. Afanas'eva and P. N. Vabishchevich and M. V. Vasil'eva},
     title = {Unconditionally stable schemes for convection-diffusion problems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--15},
     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_3_a0/}
}
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N. M. Afanas'eva; P. N. Vabishchevich; M. V. Vasil'eva. Unconditionally stable schemes for convection-diffusion problems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2013), pp. 3-15. http://geodesic.mathdoc.fr/item/IVM_2013_3_a0/