Convergence of upwind schemes for a stationary shock

Author:
Jens Lorenz

Journal:
Math. Comp. **46** (1986), 45-57

MSC:
Primary 65M10; Secondary 76-08, 76L05

DOI:
https://doi.org/10.1090/S0025-5718-1986-0815830-2

MathSciNet review:
815830

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Abstract: A nonlinear first-order boundary value problem with discontinuous solutions is considered. It arises in the study of gasflow through a duct and allows, in general, for multiple solutions. New convergence results for three difference schemes are presented and the sharpness of numerical layers is established. For the EO-scheme, stability of a physically correct solution with respect to time evolution is shown.

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DOI:
https://doi.org/10.1090/S0025-5718-1986-0815830-2

Article copyright:
© Copyright 1986
American Mathematical Society