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Convergence of finite difference schemes for symmetric Keyfitz-Kranzer system

by U. Koley and N. H. Risebro

(Report number 2012-09)

Abstract
We are concerned with the convergence of numerical schemes for the initial value problem associated to the Keyfitz-Kranzer system of equations. This system is a toy model for several important models such as in elasticity theory, magnetohydrodynamics, and enhanced oil recovery. In this paper we prove the convergence of two difference schemes. One of these schemes is shown to converge to the unique entropy solution. Finally, the convergence is illustratred by several examples.

Keywords:

@Techreport{KR12_452,
  author = {U. Koley and N. H. Risebro},
  title = {Convergence of finite difference schemes for symmetric Keyfitz-Kranzer system},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2012-09},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2012/2012-09.pdf },
  year = {2012}
}

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