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

Table 1

Rate for space for 𝑔(𝑥)=𝑥^𝜇1−𝑥^𝜇2 with 𝜇₁=7/2,𝜇₂=7/3 for Example 6 using 1st-order FEM.

𝑁	𝛾=0.4		𝛾=0.7
	Error	Rate	Error	Rate
8	2.2257𝑒−3	—	2.3272𝑒−3	—
16	4.9491𝑒−4	2.1	5.4391𝑒−4	2.1
32	1.3344𝑒−4	1.9	1.4496𝑒−4	1.9
64	3.0457𝑒−5	2.1	3.3110𝑒−5	2.1
128	7.4518𝑒−6	2.0	7.9799𝑒−6	2.1
256	1.8840𝑒−6	2.0	1.9807𝑒−6	2.0