Optimal Convergence Rates of Moving Finite Element Methods for Space-Time Fractional Differential Equations

Table 4

Rate for time for 𝑔(𝑥)=𝑥^𝜇1−𝑥^𝜇2 with 𝜇₁=7/2, 𝜇₂=7/3 for Example 7 using 3rd-order FEM.

𝑀	𝛾=0.4		𝛾=0.7
	Error	Rate	Error	Rate
16	5.9067𝑒−4	—	5.9068𝑒−4	—
32	1.1010𝑒−4	2.4	1.1011𝑒−4	2.4
64	3.2024𝑒−5	1.7	3.2025𝑒−5	1.7
128	1.3049𝑒−5	1.2	1.3049𝑒−5	1.2
256	6.4572𝑒−6	1.0	6.4572𝑒−6	1.0
512	3.1807𝑒−6	1.0	3.1808𝑒−6	1.0
1024	1.5882𝑒−6	1.0	1.5882𝑒−6	1.0
2048	7.9375𝑒−7	1.0	7.9375𝑒−7	1.0