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

Table 9

Convergence analysis of Example 4.2 by Bernstein 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	2.4186𝑒+002	1.7618𝑒−004	2.8143𝑒−004	2.7609𝑒+002	4.9906𝑒−005	1.3489𝑒−004
6	4.6720𝑒+002	2.6676𝑒−007	3.8509𝑒−007	6.8378𝑒+002	2.9181𝑒−008	7.8955𝑒−008
8	8.0785𝑒+002	2.0042𝑒−010	2.7687𝑒−010	1.4516𝑒+003	9.1270𝑒−012	2.4596𝑒−011
10	1.8803𝑒+003	1.4215𝑒−013	1.8609𝑒−013	2.6872𝑒+003	8.3967𝑒−015	1.7718𝑒−014
12	9.7253𝑒+003	6.1320𝑒−014	8.4108𝑒−014	4.4882𝑒+003	6.8128𝑒−015	1.5746𝑒−014