Skip to main content

Table 5 Numerical errors and convergence orders in spatial direction with \(\tau =\frac{1}{100}\), \(\beta =2\) and \(\alpha =0.1\) at \(T=1\) for Example 2

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 2.7798e-1 1.96 6.4097e-1 0.99 8.9179e-2 2.13 7.3655e-2 1.95
π/8 7.1673e-2 1.99 3.2382e-1 1.00 2.0417e-2 2.03 1.9064e-2 1.96
π/16 1.8050e-2 2.00 1.6239e-1 1.00 4.9828e-3 2.01 4.8843e-3 1.99
π/32 4.5193e-3 2.00 8.1256e-2 1.00 1.2363e-3 2.01 1.2298e-3 2.01
π/64 1.1288e-3 4.0636e-2 3.0656e-4 3.0615e-4