Back to Search
Start Over
The Convergence Rate of Finite Difference Schemes in the Presence of Shocks
- Source :
- SIAM Journal on Numerical Analysis. 35:2464-2485
- Publication Year :
- 1998
- Publisher :
- Society for Industrial & Applied Mathematics (SIAM), 1998.
-
Abstract
- Finite difference approximations generically have ${\cal O}(1)$ pointwise errors close to a shock. We show that this local error may effect the smooth part of the solution such that only first order is achieved even for formally higher-order methods. Analytic and numerical examples of this form of accuracy are given. We also show that a converging method will have the formal order of accuracy in domains where no characteristics have passed through a shock.
Details
- ISSN :
- 10957170 and 00361429
- Volume :
- 35
- Database :
- OpenAIRE
- Journal :
- SIAM Journal on Numerical Analysis
- Accession number :
- edsair.doi...........a11d5e2bae5671c14e085fa083735c06