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Table 2 Numerical errors and convergence orders in spatial direction with \(\tau =\frac{1}{100}\) and \(\alpha =0.1\) at \(T=1\) for Example 1

From: Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation

h \(\|u^{n}-u_{h}^{n}\|\) Rate \(\|u^{n}-u_{h}^{n}\|_{1}\) Rate \(\|I_{h}u^{n}-u_{h}^{n}\|_{1}\) Rate \(\|u^{n}-\varPi _{2h}u_{h}^{n}\|_{1}\) Rate
π/4 2.7783e-1 1.96 6.4095e-1 0.99 8.8916e-2 2.13 7.3428e-2 1.95
π/8 7.1625e-2 1.99 3.2382e-1 1.00 2.0343e-2 2.04 1.8993e-2 1.96
π/16 1.8037e-2 2.00 1.6239e-1 1.00 4.9636e-3 2.01 4.8653e-3 1.99
π/32 4.5157e-3 2.00 8.1256e-2 1.00 1.2311e-3 2.01 1.2246e-3 2.01
π/64 1.1277e-3 4.0636e-2 3.0493e-4 3.0451e-4