scholarly journals A front tracking method for conservation laws in one dimension

1992 ◽  
Vol 101 (1) ◽  
pp. 130-139 ◽  
Author(s):  
N.H Risebro ◽  
A Tveito
Keyword(s):  
Conservation Laws ◽  
Front Tracking ◽  
One Dimension ◽  
Tracking Method ◽  
Front Tracking Method

scholarly journals A Second-Order Accurate Conservative Front-Tracking Method in One Dimension

2010 ◽  
Vol 31 (6) ◽  
pp. 4795-4813 ◽  
Author(s):  
Caroline Gatti-Bono ◽  
Phillip Colella ◽  
David Trebotich
Keyword(s):  
Front Tracking ◽  
Second Order ◽  
One Dimension ◽  
Tracking Method ◽  
Front Tracking Method

scholarly journals Flux-stability for conservation laws with discontinuous flux and convergence rates of the front tracking method

2021 ◽  
Author(s):  
Adrian M Ruf
Keyword(s):  
Convergence Rate ◽  
Conservation Laws ◽  
Convergence Rates ◽  
Numerical Solutions ◽  
Stability Result ◽  
Front Tracking ◽  
Tracking Method ◽  
Front Tracking Method ◽  
Discontinuous Flux ◽  
Scalar Conservation

Abstract We prove that adapted entropy solutions of scalar conservation laws with discontinuous flux are stable with respect to changes in the flux under the assumption that the flux is strictly monotone in $u$ and the spatial dependency is piecewise constant with finitely many discontinuities. We use this stability result to prove a convergence rate for the front tracking method—a numerical method that is widely used in the field of conservation laws with discontinuous flux. To the best of our knowledge, both of these results are the first of their kind in the literature on conservation laws with discontinuous flux. We also present numerical experiments verifying the convergence rate results and comparing numerical solutions computed with the front tracking method to finite volume approximations.

Sign in / Sign up

Export Citation Format

Share Document