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

Table 8

Convergence analysis of Example 4.2 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	1.4582𝑒−003	2.8374𝑒−003	3.9362𝑒+003	5.7278𝑒−004	1.4832𝑒−003
6	1.5322𝑒+004	7.2538𝑒−006	1.3324𝑒−005	1.5295𝑒+004	1.4192𝑒−006	3.5539𝑒−006
8	8.3734𝑒+004	1.9942𝑒−008	3.4812𝑒−008	4.6202𝑒+004	1.9544𝑒−009	4.5723𝑒−009
10	4.6854𝑒+005	3.4418𝑒−011	5.7661𝑒−011	1.1468𝑒+005	2.1240𝑒−012	3.9355𝑒−012
12	4.0396𝑒+006	1.5353𝑒−013	5.0360𝑒−013	2.4580𝑒+005	2.7272𝑒−013	4.6544𝑒−013