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

Table 7

Convergence analysis of Example 4.2 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	1.4582𝑒−003	2.8374𝑒−003	9.7943𝑒+002	5.7278𝑒−004	1.4832𝑒−003
6	1.7192𝑒+003	7.2538𝑒−006	1.3324𝑒−005	2.6631𝑒+003	1.4192𝑒−006	3.5539𝑒−006
8	3.5459𝑒+003	1.9942𝑒−008	3.4812𝑒−008	5.9340𝑒+003	1.9544𝑒−009	4.5723𝑒−009
10	2.0224𝑒+004	3.4252𝑒−011	5.7468𝑒−011	1.1258𝑒+004	1.6657𝑒−012	3.6562𝑒−012
12	1.2993𝑒+005	7.4279𝑒−012	1.0651𝑒−011	2.0852𝑒+004	1.1997𝑒−014	2.0057𝑒−014