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Multiscale finite element methods for advection-diffusion problems

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Figure

Figure 2.1 Exact and numerical solutions to ( 2.15 ) for Pe H “ 8. Left: Plot on the whole domain
Table 2.4 shows the accuracy of the methods with respect to the reference solution. We see that the method ( 2.34 )–( 2.35 ) is more accurate than the method ( 2.77 )–( 2.81 ) (outside the boundary layer)
Figure 2.4 Relative errors in the single-scale case (δ “ 0.75, ε “ 1 and H “ 1{16). When α is large, the main difficulty is to capture the oscillations at scale ε
Figure 2.6 Relative error e H out 1 (δ “ 0.75, ε “ 1{128 and H “ 1{16).
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