Preprint 1998-014

Degenerate Convection-Diffusion Equations and Implicit Monotone Difference Schemes

Steinar Evje and Kenneth Hvistendahl Karlsen

Abstract: 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 schemes.

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Degenerate convection-diffusion equations and implicit monotone difference schemes
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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