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It is shown that the absolute constant in the Berry-Esseen inequality for i.i.d. Bernoulli random variables is strictly less than the Esseen constant, if 1 ≤ n ≤ 500000, where n is a number of summands. This result is got both with the help of a supercomputer and an interpolation theorem, which is proved in the paper as well. In addition, applying the method developed by S. Nagaev and V. Chebotarev in 2009-2011, an upper bound is obtained for the absolute constant in the Berry-Esseen inequality in the case under consideration, which differs from the Esseen constant by no more than 0.06%. As an auxiliary result, we prove a bound in the local Moivre-Laplace theorem which has a simple and explicit form.Despite the best possible result, obtained by J. Schulz in 2016, we propose our approach to the problem of finding the absolute constant in the Berry-Esseen inequality for two-point distributions since this approach, combining analytical methods and the use of computers, could be useful in solving other mathematical problems.Keywords Optimal value of absolute constant in Berry-Esseen inequality, binomial distribution, numerical methods 2010 MSC 60F05, 65-04

The finite element method is usually used for two-dimensional space. The paper investigates the finite element method for solving the Signorini problem in three-dimensional space.

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