An 𝐻¹-Galerkin Expanded Mixed Finite Element Approximation of Second-Order Nonlinear Hyperbolic Equations

Table 1

The errors of ‖𝑢−𝑢_ℎ‖ at different times.

Time	𝑡=0.2		𝑡=0.4		𝑡=0.8		𝑡=1.0
ℎ=Δ𝑡	Error	Order	Error	Order	Error	Order	Error	Order
1/10	0.001	⧵	0.0025	⧵	0.0075	⧵	0.0104	⧵
1/20	2.6553𝑒−4	1.9131	6.3152𝑒−4	1.9850	0.0019	1.9809	0.0026	2.0000
1/30	1.1843𝑒−4	1.9913	2.8183𝑒−4	1.9899	8.4165𝑒−4	2.0082	0.0012	1.9069
1/40	6.6744𝑒−5	1.9934	1.5903𝑒−4	1.9890	4.7373𝑒−4	1.9978	6.6038𝑒−4	2.0761
1/50	4.2788𝑒−5	1.9925	1.0212𝑒−4	1.9850	3.0325𝑒−4	1.9991	4.2104𝑒−4	2.0170