Glimm schemes

[Inge H. A. Pettersen]

In 1965 J. Glimm introduced a technique for approximations of
hyperbolic nonlinear systems that has been later known as the Glimm
scheme. What is the state of the art today with respect to this
technique? Is is still considered as a good method or are there better
methods today?

[Harald Hanche-Olsen]

+ ing...@start.no (Inge H. A. Pettersen):

It was never considered a very efficient method for numerical
computation. Glimm and his group were themselves pursuing other
numerical methods, termed front tracking methods explicitly tracking
the fronts and using higher order methods for the smooth parts of the
solutions. Another method was pioneered in Oslo, somewhat confusingly
also called front tracking. Then there is are lots of finite volume
methods.

Some random references:

Helge Holden, Nils Henrik Risebro: Front tracking for hyperbolic
conservation laws.
Randall J. LeVeque: Numerical methods for conservation laws.
Randall J. LeVeque: Finite Volume Methods for Hyperbolic Problems.

--
* Harald Hanche-Olsen <URL:http://www.math.ntnu.no/~hanche/>
- Debating gives most of us much more psychological satisfaction
than thinking does: but it deprives us of whatever chance there is
of getting closer to the truth. -- C.P. Snow

[I posted a somewhat longer followup before, but it must have gotten
lost on its way to the moderators, or something. Stupidly I did not
keep a copy around.]

[ingehap]

Thanks for your reply. Do you have any reference that compares
various techniques for hyperbolic nonlinear system with respect
to numeric efficiency and with respect to analytical properties
like convergence and stability?