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Table 1 Numerical results for Example  1 with \(\pmb{\tau=2^{-12}}\)

From: An expanded mixed finite element simulation for two-sided time-dependent fractional diffusion problem

β h 1/16 1/32 1/64 1/128 Order
1/4 \(\Vert u-u_{h} \Vert \) 9.50e−03 4.78e−03 2.40e−03 1.20e−03 1.00
\(\vert\!\vert\!\vert p-p_{h}\vert\!\vert\!\vert \) 3.33e−03 9.62e−04 2.81e−04 8.20e−05 1.78
\(\vert\!\vert\!\vert q-q_{h}\vert\!\vert\!\vert \) 4.44e−03 1.43e−03 4.62e−04 1.50e−04 1.60
1/2 \(\Vert u-u_{h} \Vert \) 9.48e−03 4.77e−03 2.39e−03 1.20e−03 1.00
\(\vert\!\vert\!\vert p-p_{h}\vert\!\vert\!\vert \) 1.43e−03 3.94e−04 1.07e−04 2.79e−05 1.92
\(\vert\!\vert\!\vert q-q_{h}\vert\!\vert\!\vert \) 3.90e−03 1.15e−03 3.45e−04 1.05e−04 1.73
2/3 \(\Vert u-u_{h} \Vert \) 1.48e−02 7.53e−03 3.78e−03 1.89e−03 1.00
\(\vert\!\vert\!\vert p-p_{h}\vert\!\vert\!\vert \) 6.15e−04 1.69e−04 4.54e−05 1.19e−05 1.94
\(\vert\!\vert\!\vert q-q_{h}\vert\!\vert\!\vert \) 3.98e−03 1.09e−03 3.02e−04 8.37e−05 1.84