Degenerate Convection-Diffusion Equations and Implicit Monotone
Steinar Evje and Kenneth Hvistendahl Karlsen
We analyse implicit monotone finite difference schemes for nonlinear, possibly
strongly degenerate, convection-diffusion equations in one spatial dimension.
Since we allow strong degeneracy, solutions can be discontinuous and are in
general not uniquely determined by their data. We thus choose to work with
weak solutions that belong to the $BV$ (in space and time) class and, in
addition, satisfy an entropy condition. The difference schemes are shown to
converge to the unique $BV$ entropy weak solution of the problem. This paper
complements our previous work on explict monotone
- Available as PostScript
- Degenerate convection-diffusion equations and implicit monotone
- Steinar Evje,
- Kenneth Hvistendahl Karlsen,
- Publishing information:
- Applied mathematics report 1998, University of Bergen, Bergen, Norway.
- Submitted by:
March 30 1998.
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