Name
Title | ||
|---|---|---|
A COMPARISON OF DUALITY AND ENERGY A POSTERIORI ESTIMATES FOR L-infinity( 0, T; L-2( Omega)) IN PARABOLIC PROBLEMS |
Abstract | ||
|---|---|---|
We use the elliptic reconstruction technique in combination with a duality approach to prove a posteriori error estimates for fully discrete backward Euler scheme for linear parabolic equations. As an application, we combine our result with the residual based estimators from the a posteriori estimation for elliptic problems to derive space-error indicators and thus a fully practical version of the estimators bounding the error in the L-infinity(0, T; L-2(Omega)) norm. These estimators, which are of optimal order, extend those introduced by Eriksson and Johnson in 1991 by taking into account the error induced by the mesh changes and allowing for a more flexible use of the elliptic estimators. For comparison with previous results we derive also an energy-based a posteriori estimate for the L-infinity(0, T; L-2(Omega))-error which simplifies a previous one given by Lakkis and Makridakis in 2006. We then compare both estimators (duality vs. energy) in practical situations and draw conclusions. |
Year | Venue | Keywords |
|---|---|---|
2015 | MATHEMATICS OF COMPUTATION | mathematical analysis,numerical analysis,parabolic equation |
DocType | Volume | Issue |
Journal | 84 | 294 |
ISSN | Citations | PageRank |
0025-5718 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Omar Lakkis | 1 | 72 | 7.05 |
| Charalambos Makridakis | 2 | 253 | 48.36 |
| Tristan Pryer | 3 | 34 | 4.17 |