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

Table 2

Convergence analysis of Example 4.1 by Bernstein 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	8.0697𝑒+002	3.2739𝑒−005	7.2959𝑒−005	9.7943𝑒+002	9.3669𝑒−006	3.5591𝑒−005
6	1.7192𝑒+003	1.0254𝑒−007	2.8205𝑒−007	2.6631𝑒+003	1.8687𝑒−008	7.6800𝑒−008
8	3.5459𝑒+003	2.7004𝑒−010	6.8954𝑒−010	5.9340𝑒+003	2.7678𝑒−011	9.5494𝑒−011
10	2.0224𝑒+004	6.0013𝑒−013	1.1492𝑒−012	1.1258𝑒+004	2.5097𝑒−014	7.5211𝑒−014
12	1.2993𝑒+005	8.5704𝑒−013	3.2062𝑒−012	2.0852𝑒+004	1.4182𝑒−015	3.3308𝑒−015