Journal of Applied Mathematics / 2012 / Article / Tab 2

Research Article

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

Table 2

Comparison of the macro-model to the micro-model for different values of πœ€ as in Example 3.3.

# cells πœ€ β€– 𝑒 𝑁 πœ€ β€– βˆ— , 𝐿 1 𝛼 1 β€– 𝑒 𝑁 πœ€ β€– βˆ— , 𝐿 2 𝛼 2

3 Γ— 3 1 / 3 1 . 1 4 4 6 Γ— 1 0 βˆ’ 2 β€” 3 . 0 7 1 5 Γ— 1 0 βˆ’ 2 β€”
5 Γ— 5 1 / 5 7 . 0 0 6 5 Γ— 1 0 βˆ’ 3 1 . 0 4 0 8 1 . 8 3 8 7 Γ— 1 0 βˆ’ 2 0 . 9 9 5 6
7 Γ— 7 1 / 7 5 . 1 5 4 1 Γ— 1 0 βˆ’ 3 1 . 0 9 5 8 1 . 3 3 6 3 Γ— 1 0 βˆ’ 2 1 . 0 5 4 3
9 Γ— 9 1 / 9 4 . 1 7 0 4 Γ— 1 0 βˆ’ 3 1 . 1 8 6 7 1 . 0 6 8 4 Γ— 1 0 βˆ’ 2 1 . 1 2 3 2
1 1 Γ— 1 1 1 / 1 1 3 . 5 7 9 4 Γ— 1 0 βˆ’ 3 1 . 3 1 3 1 9 . 0 4 6 0 Γ— 1 0 βˆ’ 3 1 . 2 0 5 8