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

Table 6

Convergence analysis of Example 4.2 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	3.5634𝑒−004	1.3781𝑒−003	1.2005𝑒+002	1.4132𝑒−005	1.0699𝑒−004
6	1.9948𝑒+003	5.6809𝑒−007	3.1820𝑒−006	5.0076𝑒+002	5.6321𝑒−009	6.2488𝑒−008
8	2.6058𝑒+004	5.3895𝑒−010	3.9608𝑒−009	6.5562𝑒+003	1.3353𝑒−012	1.9540𝑒−011
10	3.6110𝑒+005	3.4189𝑒−013	3.0718𝑒−012	9.0944𝑒+004	4.3556𝑒−014	3.5483𝑒−013
12	5.1689𝑒+006	7.9344𝑒−014	7.1592𝑒−013	1.3025𝑒+006	2.6693𝑒−014	4.7276𝑒−013