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In the present paper algorithms for constructing a finite element mesh of compound domains and minimizing the ribbon width of the system of resolving equations by the finite element method (FEM) are considered. A technology for constructing a finite element mesh by connecting elementary subdomains, a semi-automatic method for partitioning a two-dimensional multiply connected domain with a curvilinear boundary, and ordering the node numbers of a finite element mesh is described. In this case, the algorithms allow, by ordering the numbering of nodes, to determine such a sequence in which the ribbon width of non-zero coefficients of the system of resolving equations by the FEM will be locally minimal. [ABSTRACT FROM AUTHOR]