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Table 1 Numerical results of Example 1

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

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

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

1.46324e − 02

–

3.35880e − 02

–

7.31505e − 02

–

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

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

3.91388e − 03

1.90

8.18124e − 03

2.04

1.89129e − 02

1.95

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

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

9.11840e − 04

2.10

1.91874e − 03

2.09

4.64444e − 03

2.03

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

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

2.01991e − 04

2.17

3.97933e − 04

2.27

1.03486e − 03

2.17