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Approximation of solutions and derivative of singularly perturbed elliptic equation of convection-diffusion. (Russian, English) Zbl 1091.76064

Zh. Vychisl. Mat. Mat. Fiz. 43, No. 5, 672-689 (2003); translation in Comput. Math. Math. Phys. 43, No. 5, 641-657 (2003).
The author conders a boundary problem for singularly perturbed elliptic convection-diffusion equation. Classical mesh approximations are used with piecewise-uniform grids, which are stretched in a vicinity of boundary layer. Approximation error for solution and for derivatives of solution are studied in \(\rho\)-metrics, and the convergence of classical and \(\varepsilon\)-uniformly converging schemes is investigated.

MSC:

76R99 Diffusion and convection
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
35Q35 PDEs in connection with fluid mechanics
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