caa a22 4500 378884174 CHVBK 20180305123439.0 cr unu---uuuuu 161128s2004 xx s 000 0 eng 10.2478/cmam-2004-0007 doi (NATIONALLICENCE)gruyter-10.2478/cmam-2004-0007 A Class of Singularly Perturbed Convection-Diffusion Problems with a Moving Interior Layer. An a Posteriori Adaptive Mesh Technique [Elektronische Daten] 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'. 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. singular perturbation problem nationallicence convection-diffusion equation nationallicence moving interior/transition layer nationallicence a posteriori adaptive mesh nationallicence almost ε-uniform convergence nationallicence Shishkin Grigory I. Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Science, 16 S. Kovalevskaya St., 620219 Ekaterinburg, Russia Shishkina Lidia P. Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Science, 16 S. Kovalevskaya St., 620219 Ekaterinburg, Russia Hemker Pieter W. CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands Computational Methods in Applied Mathematics De Gruyter 4/1(2004), 105-127 1609-4840 4:1<105 2004 4 cmam https://doi.org/10.2478/cmam-2004-0007 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.2478/cmam-2004-0007 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Shishkin Grigory I. Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Science, 16 S. Kovalevskaya St., 620219 Ekaterinburg, Russia NATIONALLICENCE 700 1- Shishkina Lidia P. Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Science, 16 S. Kovalevskaya St., 620219 Ekaterinburg, Russia NATIONALLICENCE 700 1- Hemker Pieter W. CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands NATIONALLICENCE 773 0- Computational Methods in Applied Mathematics De Gruyter 4/1(2004), 105-127 1609-4840 4:1<105 2004 4 cmam CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter