Local error analysis for approximate solutions of hyperbolic conservation laws |
| |
Authors: | Smadar Karni Alexander Kurganov |
| |
Institution: | (1) Department of Mathematics, University of Michigan, 48109-1109 Ann Arbor, MI, USA;(2) Department of Mathematics, Tulane University, 70118 New Orleans, LA, USA |
| |
Abstract: | We consider approximate solutions to nonlinear hyperbolic conservation laws. If the exact solution is unavailable, the truncation error may be the only quantitative measure for the quality of the approximation. We propose a new way of estimating the local truncation error, through the use of localized test-functions. In the convex scalar case, they can be converted intoL
loc
estimates, following theLip convergence theory developed by Tadmor et al. Comparisons between the local truncation error and theL
loc
-error show remarkably similar behavior. Numerical results are presented for the convex scalar case, where the theory is valid, as well as for nonconvex scalar examples and the Euler equations of gas dynamics. The local truncation error has proved a reliable smoothness indicator and has been implemented in adaptive algorithms in Karni, Kurganov and Petrova, J. Comput. Phys. 178 (2002) 323–341]. |
| |
Keywords: | conservation laws weak solutions truncation error error estimates |
本文献已被 SpringerLink 等数据库收录! |
|