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Article information
2001 , Volume 6, ¹ 1, p.72-87
Shishkin G.I.
Aposteriori adapted (to the solution gradient) grids in the approximation of singularly perturbed equations of convection-diffusion
Dirichlet's problem for a parabolic equation of convection-diffusion with a small parameter of the highest derivative is considered on a segment. In order to improve the accuracy of the approximate solution consecutive a posteriori refinement of the grid is employed in subdomains determined by the gradients of intermediate discrete problems solutions. The grid solutions are corrected only in these subdomains, where uniform grids are used. Difference schemes are constructed to converge "almost -uniformly" - with an error weakly depending on the parameter .
[full text] Classificator Msc2000:- *35B25 Singular perturbations
- 35K15 Initial value problems for second-order, parabolic equations
- 65M06 Finite difference methods
- 65M12 Stability and convergence of numerical methods
- 65M50 Mesh generation and refinement
Keywords: convection-diffusion equation, singular perturbation, finite-difference schemes, adaptive grids, mesh refinement, boundary layer, mesh condensation, convergence
Author(s):
Shishkin G I
Address: Russia, Ekaterinburg
E-mail: Grigorii@shishkin.ural.ru
Bibliography link:
Shishkin G.I. Aposteriori adapted (to the solution gradient) grids in the approximation of singularly perturbed equations of convection-diffusion // Computational technologies. 2001. V. 6. ¹ 1. P. 72-87
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