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Theory and Modern Applications

Table 1 \(\Vert u-u_{N} \Vert _{\frac {1}{2},p,\varGamma_{0}}\) and \(\Vert u-u_{N} \Vert _{\frac{1}{2},*,\varGamma _{0}}\) with respect to N

From: Galerkin method for the scattering problem of strip gratings

N

2

4

8

16

32

64

\(\Vert u-u_{N} \Vert _{\frac{1}{2},p,\varGamma_{0}}\)

9.0460E–02

2.6825E–02

7.1011E–03

1.8020E–03

4.5188E–04

1.1302E–04

order

 

1.7537

1.9175

1.9785

1.9956

1.9995

\(\Vert u-u_{N} \Vert _{\frac{1}{2},*,\varGamma_{0}}\)

8.4367E–02

2.5019E–02

6.6220E–03

1.6799E–03

4.2110E–04

1.0522E–04

order

 

1.7537

1.9177

1.9788

1.9959

1.9997