A study was conducted to demonstrate variations of block-element boundaries. The block elements for the inner and outer boundary-value problem for a cylinder with a complicated boundary were constructed using the differential factorization method. It was shown that the block elements resulted in a sufficient variety of the regions occupied by them. The construction of block elements in various systems of coordinates was an important component of their use in the investigation and solution of various boundary-value problems including multidimensional ones. It was demonstrated that the block elements had a number of advantages whose possibilities considerably contributed to the investigation of solutions of the differential equations. The selection of the boundary-value problem was related to the fact that the same approach was used when investigating the boundary-value problems for sets of partial differential equations.
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