Geodesic
Convergence of discretization procedures for problems whose entropy solutions are uniquely characterized by additional relations
Applications of Mathematics, Tome 48 (2003) no. 6, pp. 417-427.

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Weak solutions of given problems are sometimes not necessarily unique. Relevant solutions are then picked out of the set of weak solutions by so-called entropy conditions. Connections between the original and the numerical entropy condition were often discussed in the particular case of scalar conservation laws, and also a general theory was presented in the literature for general scalar problems. The entropy conditions were realized by certain inequalities not generalizable to systems of equations in a trivial way. It is a concern of this article to extend the theory in such a way that inequalities can be replaced by general relations, and this not only in an abstract way but also realized by examples.
DOI : 10.1023/B:APOM.0000024483.00505.79
Classification : 35L60, 47J25, 65J15, 65N12 
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Ansorge, Rainer. Convergence of discretization procedures for problems whose entropy solutions are uniquely characterized by additional relations. Applications of Mathematics, Tome 48 (2003) no. 6, pp. 417-427. doi : 10.1023/B:APOM.0000024483.00505.79. http://geodesic.mathdoc.fr/articles/10.1023/B:APOM.0000024483.00505.79/

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