The Backward Euler Fully Discrete Finite Volume Method for the Problem of Purely Longitudinal Motion of a Homogeneous Bar

Table 3

The orders of ‖𝑢−𝑢_ℎ‖_0,ℎ and |𝑢−𝑢_ℎ|_1,ℎ.

Time	Order	For	‖𝑢−𝑢ℎ‖0,ℎ	Order	For	|𝑢−𝑢ℎ|1,ℎ
𝑡	0.05/0.025	0.025/0.0125	0.0125/0.00625	0.05/0.025	0.025/0.0125	0.0125/0.00625
0.1	0.9790	0.9947	1.0000	1.0157	1.0083	1.0050
0.2	0.9752	0.9969	1.0185	1.0142	1.0083	1.0056
0.3	0.9708	1.0000	1.0000	1.0132	1.0072	1.0021
0.4	0.9884	0.9695	0.9925	1.0118	1.0068	1.0046
0.5	0.9555	1.0000	0.9917	1.0094	1.0050	1.0025
0.6	0.9574	0.9861	1.0000	1.0083	1.0028	1.0056
0.7	0.9739	0.9846	0.9898	1.0061	1.0031	1.0000
0.8	0.9536	0.9830	1.0000	1.0034	1.0017	1.0000
0.9	0.9649	0.9812	1.0000	1.0028	1.0000	1.0000