Finite difference schemes for the symmetric Keyfitz-Kranzer system

TL;DR

This paper proves the convergence of three finite difference schemes for the symmetric Keyfitz-Kranzer system, a model relevant to elasticity, magnetohydrodynamics, and oil recovery, with two schemes converging to the entropy solution.

Contribution

It establishes the convergence of three numerical schemes for the Keyfitz-Kranzer system, including proofs for two schemes converging to the entropy solution.

Findings

Two schemes proven to converge to the entropy solution.

Convergence demonstrated through several numerical examples.

The system models important physical phenomena.

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 three difference schemes. Two of these schemes is shown to converge to the unique entropy solution. Finally, the convergence is illustrated by several examples.