A Godunov-Mixed Finite Element Method on Changing Meshes for the Nonlinear Sobolev Equations

Table 3

Convergence rate of 𝐿²-norm.

Time	Convergence rates of ‖𝑢^𝑛−𝑈^𝑛‖			Convergence rates of ‖𝐳^𝑛−𝐙^𝑛‖
	Case 1/Case 2	Case 2/Case 3	Case 3/Case 4	Case 1/Case 2	Case 2/Case 3	Case 3/Case 4
𝑡=0.4	0.9670	0.9852	1.0392	0.8052	0.9271	1.2167
𝑡=0.6	0.9023	1.0724	0.9974	0.8692	1.1121	1.0290
𝑡=1.0	0.8464	1.0075	1.0242	0.7009	0.9963	1.0007