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Table 4 Accuracy test for adaptive IMEX-RK-LDG scheme of 3D NS equations

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

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
1 4 1.76E-01 2.37E-01 1.50E-01
  8 4.61E-02 1.93 6.37E-02 1.90 3.49E-02 2.10
  16 9.07E-03 2.34 1.34E-02 2.25 6.77E-03 2.37
  32 1.81E-03 2.31 3.00E-03 2.15 1.44E-03 2.23
2 4 5.00E-02 7.46E-02 4.70E-02
  8 7.73E-03 2.69 1.02E-02 2.86 6.35E-03 2.88
  16 8.06E-04 3.26 1.16E-03 3.13 7.35E-04 3.11
  32 9.26E-05 3.12 1.40E-04 3.05 8.98E-05 3.03