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Table 2 Numerical results of Example 2

From: Convergence and superconvergence of variational discretization for parabolic bilinear optimization problems

h

k

\(|\!|\!|u-u_{h}|\!|\!|\)

Rate

\(|\!|\!|R_{h}y-y_{h}|\!|\!|_{1}\)

Rate

\(|\!|\!|R_{h}p-p_{h}|\!|\!|_{1}\)

Rate

\(\frac{1}{10}\)

\(\frac{1}{10}\)

2.45170e − 05

–

5.45644e − 04

–

3.56804e − 03

–

\(\frac{1}{20}\)

\(\frac{1}{40}\)

6.45526e − 06

1.93

1.29880e − 04

2.07

9.02173e − 04

1.98

\(\frac{1}{40}\)

\(\frac{1}{160}\)

1.72058e − 06

1.91

3.19495e − 05

2.02

2.26222e − 04

2.00

\(\frac{1}{80}\)

\(\frac{1}{640}\)

4.3535e − 07

1.98

7.85015e − 06

2.03

5.64788e − 05

2.00