Geodesic
The finite element method on adapted meshes for the two-dimensional convection diffusion problem
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 4, pp. 309-320 
B. M. Bagaev; H.-G. Roos. The finite element method on adapted meshes for the two-dimensional convection diffusion problem. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 4, pp. 309-320. http://geodesic.mathdoc.fr/item/SJVM_1999_2_4_a1/
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     title = {The finite element method on adapted meshes for the two-dimensional convection diffusion problem},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a singularly perturbed elliptic boundary value problem which models a special channel flow. Basing on the decomposition of the exact solution we obtain a priori bounds for derivatives of the exact solution. For the numerical solution, we used linear finite elements on an adapted meshes, further we discuss the additive extraction method. We obtain uniform estimates for the approximate solution in some energetic norm.

[1] Roos H.-G., Stynes M., Tobiska L., Numerical Methods for Singularly Perturbed Differential Equations, Springer-Verlag, Berlin, 1996 | MR

[2] Bagaev B. M., Shaidurov V. V., The solving of grid meshes for singular perturbed problem, Nauka, Novosibirsk, 1998 (In Russian) | MR | Zbl

[3] Dobrowolsky M., Roos H.-G., “A priori estimates for the solution of convection-diffusion problems and interpolation on Shishkin meshes”, ZAA, 16:4 (1997), 1001–1012 | MR

[4] Miller J. J. H., O'Riordan E., Shishkin G. I., Fitted Numerical Methods for Singular Perturbation Problems, Singapore, 1996

[5] Shaidurov V., Tobiska L., Special integration formulas for a convection-diffusion problem, Preprint No 40, Otto von Guericke-Universitaet, Magdeburg, 1995 | MR | Zbl

[6] Ladyshenskaya O. A., Ural'cheva N. N., Linear and quasilinear equations of elliptic type, Nauka, M., 1964 (In Russian)

[7] Stynes M., O'Riordan E., “A uniformly convergent Galerkin method on a Shishkin mesh for a convection-diffusion problem”, Journal of Mathematical Analysis and Applications, 214:1 (1996), 36–54 | DOI | MR

[8] Ciarlet P. G., Basic Error Estimates for Elliptic Problems, North-Holland, 1991 | MR

[9] Roos H.-G., “Layer adapted grids for singular perturbation problems”, ZAMM, 78:5 (1998), 291–309 | 3.0.CO;2-R class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl