Skip to main content

Table 6 Numerical errors and convergence orders in spatial direction with \(\tau =\frac{1}{100}\), \(\beta =2\) and \(\alpha =0.3\) 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 2.7064e-1 1.96 6.4016e-1 0.98 7.6732e-2 2.18 6.2915e-2 2.00
π/8 6.9390e-2 1.99 3.2374e-1 1.00 1.6960e-2 2.05 1.5732e-2 1.97
π/16 1.7445e-2 2.00 1.6238e-1 1.00 4.0926e-3 2.02 4.0023e-3 2.00
π/32 4.3629e-3 2.01 8.1255e-2 1.00 1.0084e-3 2.04 1.0024e-3 2.03
π/64 1.0865e-3 4.0636e-2 2.4562e-4 2.4523e-4