Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model

Table 6

Sensitivity of the macro-model solution to the grid used to compute 𝑐_ℎ𝑐≈𝑐 and 𝑘̃_1,ℎ𝑘1≈𝑘̃₁ as Example 3.7.

ℎ^𝑐−1	𝑐ℎ𝑐	‖𝑒^𝑁𝜀‖∗,𝐿1	‖𝑒^𝑁𝜀‖∗,𝐿2
10	1.9000×10^−3	3.6251×10^−2	5.9026×10^−2
50	1.8370×10^−3	3.6251×10^−2	5.9026×10^−2
100	1.8292×10^−3	3.6251×10^−2	5.9026×10^−2
200	1.8258×10^−3	3.6251×10^−2	5.9026×10^−2
ℎ^𝑘−1	𝑘̃1(1,1)	‖𝑒^𝑁𝜀‖∗,𝐿1	‖𝑒^𝑁𝜀‖∗,𝐿2
10	4.6306×10^−1	3.5392×10^−2	5.7835×10^−2
50	4.5141×10^−1	3.6222×10^−2	5.8989×10^−2
100	4.5046×10^−1	3.6301×10^−2	5.9093×10^−2
200	4.5009×10^−1	3.6332×10^−2	5.9134×10^−2