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

Table 1

Convergence analysis of Example 4.1 by Galerkin formulation.

𝑁	𝛽1=100, 𝛽2=10			𝛽1=10, 𝛽2=100
	Cond	‖𝑢−𝑈‖𝐿2	‖𝑢−𝑈‖𝐻1	Cond	‖𝑢−𝑈‖𝐿2	‖𝑢−𝑈‖𝐻1
4	2.8902𝑒+002	8.0336𝑒−006	3.1656𝑒−005	1.2005𝑒+002	6.0268𝑒−007	4.4909𝑒−006
6	1.9948𝑒+003	1.2627𝑒−008	7.1402𝑒−008	5.0076𝑒+002	2.3531𝑒−010	2.6075𝑒−009
8	2.6058𝑒+004	1.1896𝑒−011	8.7994𝑒−011	6.5562𝑒+003	5.5614𝑒−014	8.1463𝑒−013
10	3.6110𝑒+005	8.9538𝑒−014	7.2848𝑒−013	9.0944𝑒+004	1.2798𝑒−014	2.0911𝑒−013
12	5.1689𝑒+006	5.7748𝑒−014	5.2493𝑒−013	1.3025𝑒+006	5.5197𝑒−015	8.2017𝑒−014