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AN EQUAL-AREA METHOD FOR SCALAR CONSERVATION LAWS

Part of: Hyperbolic equations and systems

Published online by Cambridge University Press:  28 May 2012

MARJETA KRAMAR FIJAVŽ ,
MITJA LAKNER  and
MARJETA ŠKAPIN RUGELJ
MARJETA KRAMAR FIJAVŽ
Affiliation:
Faculty of Civil and Geodetic Engineering, University of Ljubljana, Jamova 2, 1000 Ljubljana, Slovenia (email: mkramar@fgg.uni-lj.si, mlakner@fgg.uni-lj.si, mskapin@fgg.uni-lj.si)
MITJA LAKNER
Affiliation:
Faculty of Civil and Geodetic Engineering, University of Ljubljana, Jamova 2, 1000 Ljubljana, Slovenia (email: mkramar@fgg.uni-lj.si, mlakner@fgg.uni-lj.si, mskapin@fgg.uni-lj.si)
MARJETA ŠKAPIN RUGELJ*
Affiliation:
Faculty of Civil and Geodetic Engineering, University of Ljubljana, Jamova 2, 1000 Ljubljana, Slovenia (email: mkramar@fgg.uni-lj.si, mlakner@fgg.uni-lj.si, mskapin@fgg.uni-lj.si)
*
✉For correspondence; e-mail: mskapin@fgg.uni-lj.si
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Abstract

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We study the one-dimensional conservation law. We use a characteristic surface to define a class of functions, within which the integral version of the conservation law is solved in a simple and direct way. A simple algorithm for computing the unique solution is developed. The method uses the equal-area principle and yields the solution for any given time directly.

Keywords

conservation lawequal areacharacteristicsmesh free

MSC classification

Secondary: 35L65: Conservation laws
Type
Research Article
Information
The ANZIAM Journal , Volume 53 , Issue 2 , October 2011 , pp. 156 - 170
Copyright
Copyright © Australian Mathematical Society 2012

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