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Journal of Applied Mathematics
/
2012
/
Article
/
Tab 1
/
Research Article
Bernstein-Polynomials-Based Highly Accurate Methods for One-Dimensional Interface Problems
Table 1
Convergence analysis of Example
4.1
by Galerkin formulation.
𝑁
𝛽
1
=
1
0
0
,
𝛽
2
=
1
0
𝛽
1
=
1
0
,
𝛽
2
=
1
0
0
Cond
‖
𝑢
−
𝑈
‖
𝐿
2
‖
𝑢
−
𝑈
‖
𝐻
1
Cond
‖
𝑢
−
𝑈
‖
𝐿
2
‖
𝑢
−
𝑈
‖
𝐻
1
4
2
.
8
9
0
2
𝑒
+
0
0
2
8
.
0
3
3
6
𝑒
−
0
0
6
3
.
1
6
5
6
𝑒
−
0
0
5
1
.
2
0
0
5
𝑒
+
0
0
2
6
.
0
2
6
8
𝑒
−
0
0
7
4
.
4
9
0
9
𝑒
−
0
0
6
6
1
.
9
9
4
8
𝑒
+
0
0
3
1
.
2
6
2
7
𝑒
−
0
0
8
7
.
1
4
0
2
𝑒
−
0
0
8
5
.
0
0
7
6
𝑒
+
0
0
2
2
.
3
5
3
1
𝑒
−
0
1
0
2
.
6
0
7
5
𝑒
−
0
0
9
8
2
.
6
0
5
8
𝑒
+
0
0
4
1
.
1
8
9
6
𝑒
−
0
1
1
8
.
7
9
9
4
𝑒
−
0
1
1
6
.
5
5
6
2
𝑒
+
0
0
3
5
.
5
6
1
4
𝑒
−
0
1
4
8
.
1
4
6
3
𝑒
−
0
1
3
10
3
.
6
1
1
0
𝑒
+
0
0
5
8
.
9
5
3
8
𝑒
−
0
1
4
7
.
2
8
4
8
𝑒
−
0
1
3
9
.
0
9
4
4
𝑒
+
0
0
4
1
.
2
7
9
8
𝑒
−
0
1
4
2
.
0
9
1
1
𝑒
−
0
1
3
12
5
.
1
6
8
9
𝑒
+
0
0
6
5
.
7
7
4
8
𝑒
−
0
1
4
5
.
2
4
9
3
𝑒
−
0
1
3
1
.
3
0
2
5
𝑒
+
0
0
6
5
.
5
1
9
7
𝑒
−
0
1
5
8
.
2
0
1
7
𝑒
−
0
1
4