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Two grid hp version discontinuous Galerkin finite element methods for quasi Newtonian fluid flows

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Figure 1. Example 1. (a) Comparison of the error in the DGnorm, using the standard (u∗ = uh,k, p∗ = ph,k) and both two-grid methods (u∗ = u2G,p∗ = p2G), with respect to the numberof degrees of freedom; (b) Comparison of number of degrees offreedom in the coarse and fine mesh.
Figure 2. Example 1. Cumulative CPU timing of the standard(u∗ = uh,k,p∗ = ph,k) and both two-grid (u∗ = u2G,p∗ = p2G)solvers compared to the error in the DG norm.
Figure 4. Example 1. Coarse and fine mesh after 13mesh refinements: (a) & (b) Coarse and fine mesh, respectively,for first two-grid method (Section 3); (c) & (d) Coarse and fine h-adaptivemesh, respectively, for second two-grid method (Section 4)
Figure 5. Example 1. Coarse and fine mesh after 13mesh refinements: (a) & (b) Coarse and fine mesh, respectively,for first two-grid method (Section 3); (c) & (d) Coarse and fine hp-adaptivemesh, respectively, for second two-grid method (Section 4)
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