An efficient adaptive grid method for a system of singularly perturbed convection-diffusion problems with Robin boundary conditions

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 4 Numerical results with \(\varepsilon _{1}=10^{-4}\) for Example 2

\(\varepsilon _{2}\)		N = 32	N = 64	N = 128	N = 256	N = 512	N = 1024
10⁻²	\(E_{\varepsilon _{1},\varepsilon _{2}}^{N}\)	1.99e–02	1.13e–02	6.12e–03	3.10e–03	1.48e–03	6.48e–04
10⁻²	\(r_{\varepsilon _{1},\varepsilon _{2}}^{N}\)	0.82	0.88	0.98	1.06	1.19
10⁻⁴	\(E_{\varepsilon _{1},\varepsilon _{2}}^{N}\)	2.07e–02	1.16e–02	6.05e–03	2.96e–03	1.43e–03	6.09e–04
10⁻⁴	\(r_{\varepsilon _{1},\varepsilon _{2}}^{N}\)	0.84	0.93	1.03	1.05	1.23
10⁻⁶	\(E_{\varepsilon _{1},\varepsilon _{2}}^{N}\)	2.22e–02	1.21e–02	6.29e–03	3.17e–03	1.49e–03	6.29e–04
10⁻⁶	\(r_{\varepsilon _{1},\varepsilon _{2}}^{N}\)	0.88	0.94	0.99	1.09	1.24
10⁻⁸	\(E_{\varepsilon _{1},\varepsilon _{2}}^{N}\)	2.19e–02	1.21e–02	6.32e–03	3.16e–03	1.49e–03	6.29e–04
10⁻⁸	\(r_{\varepsilon _{1},\varepsilon _{2}}^{N}\)	0.86	0.94	1.00	1.08	1.24
10⁻¹⁰	\(E_{\varepsilon _{1},\varepsilon _{2}}^{N}\)	2.17e–02	1.21e–02	6.45e–03	3.17e–03	1.49e–03	6.31e–04
10⁻¹⁰	\(r_{\varepsilon _{1},\varepsilon _{2}}^{N}\)	0.84	0.91	1.02	1.09	1.24