Bernstein-Polynomials-Based Highly Accurate Methods for One-Dimensional Interface Problems

Table 3

Convergence analysis of Example 4.1 by Lagrange collocation method (𝛽₁=100, 𝛽₂=10).

𝑁	Equidistant collocation points			L-G-L collocation points
	Cond	‖𝑢−𝑈‖𝐿2	‖𝑢−𝑈‖𝐻1	Cond	‖𝑢−𝑈‖𝐿2	‖𝑢−𝑈‖𝐻1
4	3.3057𝑒+003	5.2000𝑒−005	7.2298𝑒−005	3.9362𝑒+003	1.4511𝑒−005	2.8433𝑒−005
6	1.5322𝑒+004	1.9556𝑒−007	2.7515𝑒−007	1.5295𝑒+004	3.1861𝑒−008	5.9502𝑒−008
8	8.3734𝑒+004	4.5539𝑒−010	6.4269𝑒−010	4.6202𝑒+004	3.9798𝑒−011	7.1989𝑒−011
10	4.6854𝑒+005	6.4179𝑒−013	9.4096𝑒−013	1.1468𝑒+005	1.8912𝑒−014	4.8567𝑒−014
12	4.0396𝑒+006	8.1907𝑒−014	1.8001𝑒−013	2.4580𝑒+005	2.2058𝑒−014	3.3532𝑒−014