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 [Java Applet] 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 [Java Applet]-uniformly" - with an error weakly depending on the parameter [Java Applet].

[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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