Pointwise error estimates for relaxation approximations to conservation laws
| dc.contributor.author | TADMOR, EITAN | |
| dc.contributor.author | TANG, TAO | |
| dc.date.accessioned | 2008-10-20T17:59:36Z | |
| dc.date.available | 2008-10-20T17:59:36Z | |
| dc.date.issued | 2000 | |
| dc.description.abstract | We obtain sharp pointwise error estimates for relaxation approximation to scalar conservation laws with piecewise smooth solutions. We first prove that the first-order partial derivatives for the perturbation solutions are uniformly upper bounded (the so-called Lip+ stability). A one-sided interpolation inequality between classical L1 error estimates and Lip+ stability bounds enables us to convert a global L1 result into a (nonoptimal) local estimate. Optimal error bounds on the weighted error then follow from the maximum principle for weakly coupled hyperbolic systems. The main difficulties in obtaining the Lip+ stability and the optimal pointwise errors are how to construct appropriate “difference functions” so that the maximum principle can be applied. | en |
| dc.format.extent | 193650 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.citation | E. Tadmor & T. Tang (2001). Pointwise error estimates for relaxation approximations to conservation laws. SIAM Journal on Mathematical Analysis 32 (2001), 870-886. | en |
| dc.identifier.uri | http://hdl.handle.net/1903/8647 | |
| dc.language.iso | en_US | en |
| dc.publisher | Copyright: Society for Industrial and Applied Mathematics | en |
| dc.relation.isAvailableAt | College of Computer, Mathematical & Physical Sciences | en_us |
| dc.relation.isAvailableAt | Mathematics | en_us |
| dc.relation.isAvailableAt | Digital Repository at the University of Maryland | en_us |
| dc.relation.isAvailableAt | University of Maryland (College Park, MD) | en_us |
| dc.subject | conservation laws | en |
| dc.subject | error estimates | en |
| dc.subject | relaxation method | en |
| dc.subject | optimal convergence rate | en |
| dc.subject | one-sided interpolation inequality | en |
| dc.subject | maximum principle | en |
| dc.title | Pointwise error estimates for relaxation approximations to conservation laws | en |
| dc.type | Article | en |