A Class of Singularly Perturbed Convection-Diffusion Problems with a Moving Interior Layer. An a Posteriori Adaptive Mesh Technique
| LEADER | caa a22 4500 | ||
|---|---|---|---|
| 001 | 378884174 | ||
| 003 | CHVBK | ||
| 005 | 20180305123439.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 161128s2004 xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.2478/cmam-2004-0007 |2 doi |
| 035 | |a (NATIONALLICENCE)gruyter-10.2478/cmam-2004-0007 | ||
| 245 | 0 | 2 | |a A Class of Singularly Perturbed Convection-Diffusion Problems with a Moving Interior Layer. An a Posteriori Adaptive Mesh Technique |h [Elektronische Daten] |
| 520 | 3 | |a We study numerical approximations for a class of singularly perturbed convection-diffusion type problems with a moving interior layer. In a domain (segment) with a moving interface between two subdomains, we consider an initial boundary value problem for a singularly perturbed parabolic convection-diffusion equation. Convection fluxes on the subdomains are directed towards the interface. The solution of this problem has a moving transition layer in the neighbourhood of the interface. Unlike problems with a stationary layer, the solution exhibits singular behaviour also with respect to the time variable. Well-known upwind finite difference schemes for such problems do not converge ε-uniformly in the uniform norm. In the case of rectangular meshes which are (a priori or a posteriori ) locally condensed in the transition layer. However, the condition for convergence can be considerably weakened if we take the geometry of the layer into account, i.e., if we introduce a new coordinate system which captures the interface. For the problem in such a coordinate system, one can use either an a priori, or an a posteriori adaptive mesh technique. Here we construct a scheme on a posteriori adaptive meshes (based on the solution gradient), whose solution converges ‘almost ε-uniformly'. | |
| 540 | |a This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. | ||
| 690 | 7 | |a singular perturbation problem |2 nationallicence | |
| 690 | 7 | |a convection-diffusion equation |2 nationallicence | |
| 690 | 7 | |a moving interior/transition layer |2 nationallicence | |
| 690 | 7 | |a a posteriori adaptive mesh |2 nationallicence | |
| 690 | 7 | |a almost ε-uniform convergence |2 nationallicence | |
| 700 | 1 | |a Shishkin |D Grigory I. |u Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Science, 16 S. Kovalevskaya St., 620219 Ekaterinburg, Russia | |
| 700 | 1 | |a Shishkina |D Lidia P. |u Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Science, 16 S. Kovalevskaya St., 620219 Ekaterinburg, Russia | |
| 700 | 1 | |a Hemker |D Pieter W. |u CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands | |
| 773 | 0 | |t Computational Methods in Applied Mathematics |d De Gruyter |g 4/1(2004), 105-127 |x 1609-4840 |q 4:1<105 |1 2004 |2 4 |o cmam | |
| 856 | 4 | 0 | |u https://doi.org/10.2478/cmam-2004-0007 |q text/html |z Onlinezugriff via DOI |
| 908 | |D 1 |a research article |2 jats | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.2478/cmam-2004-0007 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Shishkin |D Grigory I. |u Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Science, 16 S. Kovalevskaya St., 620219 Ekaterinburg, Russia | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Shishkina |D Lidia P. |u Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Science, 16 S. Kovalevskaya St., 620219 Ekaterinburg, Russia | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Hemker |D Pieter W. |u CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Computational Methods in Applied Mathematics |d De Gruyter |g 4/1(2004), 105-127 |x 1609-4840 |q 4:1<105 |1 2004 |2 4 |o cmam | ||
| 900 | 7 | |b CC0 |u http://creativecommons.org/publicdomain/zero/1.0 |2 nationallicence | |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-gruyter | ||