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

Table 5

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

𝑁	Equidistant collocation points			C-G-L collocation points
	Cond	‖𝑢−𝑈‖𝐿2	‖𝑢−𝑈‖𝐻1	Cond	‖𝑢−𝑈‖𝐿2	‖𝑢−𝑈‖𝐻1
4	9.8076𝑒+002	1.3416𝑒−005	1.8145𝑒−005	1.1152𝑒+003	3.7065𝑒−006	6.8234𝑒−006
6	4.1388𝑒+003	1.4350𝑒−008	1.9575𝑒−008	4.6618𝑒+003	1.5692𝑒−009	3.5133𝑒−009
8	2.0589𝑒+004	9.1456𝑒−012	1.2443𝑒−011	1.4939𝑒+004	3.9966𝑒−013	1.0327𝑒−012
10	1.2877𝑒+005	1.4536𝑒−014	2.5636𝑒−014	3.8643𝑒+004	1.8444𝑒−014	2.2488𝑒−014
12	1.4925𝑒+006	2.5445𝑒−013	3.2439𝑒−013	8.5365𝑒+004	1.5287𝑒−014	2.1577𝑒−014