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Table 4 Accuracies in solution values with quasi-variable meshes in Example 5.3

From: A fourth-order accurate quasi-variable mesh compact finite-difference scheme for two-space dimensional convection-diffusion problems

L  + 1 \(\boldsymbol {\tilde{\alpha}}\) \(\boldsymbol {\tilde{\beta}}\) \(\boldsymbol {\mathcal{E}_{\infty}}\) \(\boldsymbol {\mathcal{E}_{2}}\) \(\boldsymbol {\Theta_{\infty}}\) \(\boldsymbol {\Theta_{2}}\)
\(R_{e} =1\)       
4 6.75 1.15 1.18e−02 9.94e−03
8 0.70 0.60 1.08e−03 4.41e−04 4.1 4.5
16 0.12 0.10 8.65e−05 2.05e−05 3.6 4.4
\(R_{e} =10\)       
4 6.75 1.15 1.77e−02 9.74e−03
8 0.70 0.60 1.08e−03 4.41e−04 4.0 4.5
16 0.12 0.10 8.65e−05 2.05e−05 3.6 4.4
\(R_{e} = 10^{3}\)       
4 6.75 1.15 3.24e−02 2.38e−02
8 0.70 0.60 1.08e−03 4.41e−04 4.9 5.8
16 0.12 0.10 8.55e−05 2.02e−05 3.7 4.4
\(R_{e} = 10^{4}\)       
4 6.75 1.15 1.36e−02 8.63e−03
8 0.70 0.60 1.08e−03 4.41e−04 3.7 4.3
16 0.12 0.10 7.57e−05 1.86e−05 3.8 4.6