Shishkin, G. I. 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. Reviewer: Andrei Zemskov (Moskva) Cited in 1 Document MSC: 76R99 Diffusion and convection 76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics 35Q35 PDEs in connection with fluid mechanics Keywords:grid approximation; uniform convergence PDFBibTeX XMLCite \textit{G. I. Shishkin}, Zh. Vychisl. Mat. Mat. Fiz. 43, No. 5, 672--689 (2003; Zbl 1091.76064); translation in Comput. Math. Math. Phys. 43, No. 5, 641--657 (2003)