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Table 3 Numerical results for Example  2 with \(\pmb{\tau=2^{-10}}\)

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 \(\Vert u-u_{h} \Vert \) 3.62e−02 1.91e−02 9.77e−03 4.95e−03 0.99
\(\vert\!\vert\!\vert p-p_{h}\vert\!\vert\!\vert \) 6.51e−02 3.84e−02 2.28e−02 1.35e−02 0.75
\(\vert\!\vert\!\vert q-q_{h}\vert\!\vert\!\vert \) 1.13e−02 7.26e−03 4.69e−03 3.04e−03 0.63
1/2 \(\Vert u-u_{h} \Vert \) 3.62e−02 1.91e−02 9.77e−03 4.95e−03 0.99
\(\vert\!\vert\!\vert p-p_{h}\vert\!\vert\!\vert \) 1.84e−02 9.04e−03 4.48e−03 2.23e−03 1.00
\(\vert\!\vert\!\vert q-q_{h}\vert\!\vert\!\vert \) 1.03e−02 6.11e−03 3.62e−03 2.15e−03 0.75
2/3 \(\Vert u-u_{h} \Vert \) 3.62e−02 1.91e−02 9.77e−03 4.95e−03 0.99
\(\vert\!\vert\!\vert p-p_{h}\vert\!\vert\!\vert \) 6.86e−03 2.99e−03 1.31e−03 5.82e−04 1.15
\(\vert\!\vert\!\vert q-q_{h}\vert\!\vert\!\vert \) 8.18e−03 4.59e−03 2.58e−03 1.46e−03 0.82