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Continuous dependence and error estimation for viscosity methods

Published online by Cambridge University Press:  29 July 2003

Bernardo Cockburn
Bernardo Cockburn
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA E-mail: [email protected]
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Abstract

In this paper, we review some ideas on continuous dependence results for the entropy solution of hyperbolic scalar conservation laws. They lead to a complete L^\infty(L^1)-approximation theory with which error estimates for numerical methods for this type of equation can be obtained. The approach we consider consists in obtaining continuous dependence results for the solutions of parabolic conservation laws and deducing from them the corresponding results for the entropy solution. This is a natural approach, as the entropy solution is nothing but the limit of solutions of parabolic scalar conservation laws as the viscosity coefficient goes to zero.

Type
Research Article
Information
Acta Numerica , Volume 12 , May 2003 , pp. 127 - 180
Copyright
© Cambridge University Press 2003

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