An Iterative Method for Problems with Multiscale Conductivity

Table 1

The 𝐿² errors for the model (a). Ω: the whole domain, Ω_𝐼: the region inside the circle, ‖𝑢−𝑈_ℎ‖_𝐷: errors of voltage (solution) in the region 𝐷, ‖𝐽−𝐽_ℎ‖_𝐷: errors of current density (computed from voltage) in the region 𝐷, and Iter.: number of iterations.

𝑁	‖𝑢−𝑈ℎ‖Ω	‖𝑢−𝑈ℎ‖Ω𝐼	‖𝐽−𝐽ℎ‖Ω	‖𝐽−𝐽ℎ‖Ω𝐼	Iter.
16	0.0081	0.0000	0.0692	0.0157	4
32	0.0046	0.0145	0.0692	0.5800	6
64	0.0033	0.0070	0.0548	0.5347	10
128	0.0017	0.0038	0.0340	0.2208	38
256	0.0007	0.0001	0.0324	0.0061	164