Convergence of discretization procedures for problems whose entropy solutions are uniquely characterized by additional relations

Ansorge, Rainer. "Convergence of discretization procedures for problems whose entropy solutions are uniquely characterized by additional relations." Applications of Mathematics 48.6 (2003): 417-427. <http://eudml.org/doc/33157>.

@article{Ansorge2003,
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.},
author = {Ansorge, Rainer},
journal = {Applications of Mathematics},
keywords = {entropy condition},
language = {eng},
number = {6},
pages = {417-427},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convergence of discretization procedures for problems whose entropy solutions are uniquely characterized by additional relations},
url = {http://eudml.org/doc/33157},
volume = {48},
year = {2003},
}

TY - JOUR
AU - Ansorge, Rainer
TI - Convergence of discretization procedures for problems whose entropy solutions are uniquely characterized by additional relations
JO - Applications of Mathematics
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 6
SP - 417
EP - 427
AB - 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.
LA - eng
KW - entropy condition
UR - http://eudml.org/doc/33157
ER -