Convergence of Discretization Procedures for Problems Whose Entropy Solutions are Uniquely Characterized by Additional Relations |
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Authors: | Reiner Ansorge |
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Institution: | (1) Department of Mathematics, University of Hamburg, Bundesstr. 55, D-20146 Hamburg, Germany |
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Abstract: | 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. |
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