Supercloseness Result of Higher Order FEM/LDG Coupled Method for Solving Singularly Perturbed Problem on S-Type Mesh

Table 2

History of convergence of the FEM/LDG coupled method, 𝜀=10⁻⁶.

𝑘	𝑁	|||𝑢−𝑢𝑁|||𝜀				|||𝑢𝐼−𝑢𝑁|||𝜀
		S-mesh		B-S mesh		S-mesh		B-S mesh
		Error	ln-ord	Error	ord	Error	ln-ord	Error	ord
1	16	2.060𝑒−01	—	9.204𝑒−02	—	3.539𝑒−02	—	6.912𝑒−03	—
	32	1.304𝑒−01	0.97	4.750𝑒−02	0.95	1.429𝑒−02	1.93	2.069𝑒−03	1.74
	64	7.868𝑒−02	0.99	2.412𝑒−02	0.98	5.217𝑒−03	1.97	6.378𝑒−04	1.70
	128	4.599𝑒−02	1.00	1.216𝑒−02	0.99	1.785𝑒−03	1.99	2.051𝑒−04	1.64
	256	2.630𝑒−02	1.00	6.101𝑒−03	1.00	5.846𝑒−04	2.00	6.845𝑒−05	1.58
	512	1.480𝑒−02	1.00	3.057𝑒−03	1.00	1.854𝑒−04	2.00	2.344𝑒−05	1.55
2	16	4.230𝑒−02	—	8.054𝑒−03	—	6.413𝑒−03	—	7.305𝑒−04	—
	32	1.740𝑒−02	1.89	2.151𝑒−03	1.90	1.681𝑒−03	2.85	1.022𝑒−04	2.84
	64	6.406𝑒−03	1.96	5.553𝑒−04	1.95	3.744𝑒−04	2.94	1.360𝑒−05	2.91
	128	2.198𝑒−03	1.98	1.410𝑒−04	1.98	7.518𝑒−05	2.98	1.777𝑒−06	2.94
	256	7.199𝑒−04	1.99	3.554𝑒−05	1.99	1.409𝑒−05	2.99	2.325𝑒−07	2.93
	512	2.280𝑒−04	2.00	8.919𝑒−06	1.99	2.510𝑒−06	3.00	3.267𝑒−08	2.83