An explicit upwind finite element method is given for the numerical computation to multi-dimensional scalar conservation laws. It is proved that this scheme is consistent to the equation and monotone, and the approximate solution satisfies discrete entropy inequality. To guarantee the limit of approximate solutions to be a measure valued solution, we prove an energy estimate. Then the Lp strong convergence of this scheme is proved.
|Original language||English (US)|
|Number of pages||14|
|Journal||Journal of Computational Mathematics|
|State||Published - Jan 2001|
All Science Journal Classification (ASJC) codes
- Computational Mathematics