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Monotone Difference Schemes for Diffusion‐Convection Problems
Author(s) -
Stoyan Gisbert
Publication year - 1979
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19790590805
Subject(s) - convection–diffusion equation , monotone polygon , mathematics , diffusion , convection , scheme (mathematics) , mathematical analysis , physics , mechanics , geometry , thermodynamics
Monotone difference schemes are considered (that is schemes for which the maximum principle holds) for diffusion‐convection problems modelled by (1) or by corresponding parabolic and two‐dimensional elliptic equations. The diffusion/convection ratio may be small or great, and a continuous connection is created between these two cases. For instance, in one of the variants a continuous transition is achieved from the Crank‐Nicholson‐scheme (applied if convection is zero) and a symmetric, second order Wendroff scheme (for the pure transport equation.) Numerical results for (1) show the efficiency of the method.