Abstract
In this short article, we recalculate the numerical example in Křížek and Neittaanmäki (1987) for the Poisson solution u=xσ(1−x)sinπy in the unit square S as 
. By the finite difference method, an error analysis for such a problem is given from our previous study by 
where h is the meshspacing of the uniform square grids used, and C1 and C2 are two positive constants. Let ε=u−u
h
, where u
h
is the finite difference solution, and 
is the discrete H1 norm. Several techniques are employed to confirm the reduced rate 
of convergence, and to give the constants, C1=0.09034 and C2=0.002275 for a stripe domain. The better performance for arises from the fact that the constant C1 is much large than C2, and the h in computation is not small enough.
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References
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Acknowledgments.
We are grateful to Prof. M. Křížek for his communication, which has drawn our attention to study the problem in [1], and for his valuable suggestions on the original manuscript. We also express our thanks to the referees for their helpful comments and suggestions.
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Hu, HY., Li, ZC. Verification of Reduced Convergence Rates. Computing 74, 67–73 (2005). https://doi.org/10.1007/s00607-004-0079-x
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DOI: https://doi.org/10.1007/s00607-004-0079-x