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Table 1 Accuracy test for adaptive IMEX-RK-LDG scheme of 2D NS equations

From: Adaptive local discontinuous Galerkin methods with semi-implicit time discretizations for the Navier-Stokes equations

Re k N \(\phantom {\dot {i}\!}\|\rho - \rho _{h}\|_{L^{2}}\) Order \(\phantom {\dot {i}\!}\|\mathbf {u}-\mathbf {u}_{h}\|_{L^{2}}\) Order \(\phantom {\dot {i}\!}\|p-p_{h}\|_{L^{2}}\) Order
200 1 16 4.93E-03 2.72E-02 8.78E-03
   32 1.04E-03 2.24 6.15E-03 2.14 1.81E-03 2.27
   64 2.34E-04 2.15 1.44E-03 2.09 4.08E-04 2.14
   128 5.61E-05 2.02 3.51E-04 2.03 9.86E-05 2.05
  2 16 6.57E-04 3.17E-03 1.13E-03
   32 8.52E-05 2.94 3.82E-04 3.05 1.40E-04 3.01
   64 1.07E-05 2.99 4.76E-05 3.00 1.76E-05 2.99
   128 1.28E-06 3.06 5.96E-06 3.00 2.16E-06 3.02
1000 1 16 4.51E-03 2.39E-02 8.05E-03
   32 1.03E-03 2.11 5.84E-03 2.03 1.81E-03 2.14
   64 2.50E-04 2.05 1.40E-03 2.05 4.38E-04 2.05
   128 6.20E-05 2.01 3.46E-04 2.02 1.08E-04 2.01
  2 16 6.75E-04 3.32E-03 1.23E-03
   32 8.47E-05 2.99 3.94E-04 3.07 1.51E-04 3.02
   64 1.08E-05 2.96 4.86E-05 3.02 1.90E-05 2.99
   128 1.36E-06 3.00 6.02E-06 3.01 2.37E-06 3.00
5000 1 16 4.51E-03 2.39E-02 8.10E-03
   32 1.03E-03 2.12 5.83E-03 2.03 1.82E-03 2.15
   64 2.50E-04 2.05 1.40E-03 2.05 4.39E-04 2.05
   128 6.19E-05 2.01 3.46E-04 2.01 1.08E-04 2.01
  2 16 6.93E-04 3.65E-03 1.27E-03
   32 8.67E-05 3.00 4.44E-04 3.03 1.56E-04 3.02
   64 1.06E-05 3.02 5.18E-05 3.09 1.94E-05 3.00
   128 1.35E-06 2.98 6.24E-06 3.05 2.43E-06 3.00