The report outlines the basis for theory of the block element method, and shows the role of automorphism of topological manifolds in its construction. We discuss the relation of the method with other approaches, methods of finite and boundary elements, and give examples for applications of the method to problems of solid mechanics and in other areas. In particular, it is shown how to build block elements in quantum mechanics, in four-dimensional spaces of non-stationary boundary-value problems, and for modeling a terrain with tectonic faults to assess the tension of lithospheric plates.
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