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Analysis of a stabilized penalty free nitsche method for the brinkman, stokes, and darcy problems

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Figure 2. In each plot, we compare the errors varying the GLS stabilization parameter α (orange: 0.1, yellow: 1, purple: 10), the Grad-Div stabilization parameter δ (dashed line: 0.1, solid line: 1, dotted line: 10) and the characteristic length L 0 .
Figure 3 depicts the velocity profile (u 1 (y)) for a few values of µ eff and σ. Notice that, for smaller values of the ratio µ σ eff , the solution has a boundary layer near the Dirichlet boundaries
Figure 4. Example I: Error in the mesh dependent norm (2.12) against the mesh size (in double logarithmic scale), for the cases (µ eff , σ) = (1, 1) (left) and (µ eff , σ) = (0.001, 10) (right).
Figure 5. Example I: Velocity and pressure errors against the mesh size (in double logarithmic scale), for the case (µ eff , σ) = (1, 1), The lines with slope equal to 1 (dashed), 3 2 (dotted) and 2 (solid) are also shown.
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