Nefodova I. Choosing the Optimal Basis Functions and Nodes in Finite Element Method (Rectangular Elements) in the Mathematical Modeling of Heat Distribution.

The process of heat distribution in flat areas. Research and development of optimal choice method for the FEM grid nodes using interlination functions (rectangular elements) and its application to solving problems of heat conduction. General methods of functional analysis, computational mathematics, the theory of approximation of functions of several variables using the interlination concept. The theoretical value enables using interlination functions concept when building structures approximate solution of the boundary problem for adaptive selection of nodes, as well as the application of functional energy calculated for each element of the partition area of integration. The practical significance of the results is the ability to develop software, based on the proposed methods, algorithms and schemes for the approximate solution of one- and two-dimensional boundary problems of heat conduction with a minimal number of unknown parameters. The novelty of the results is in creating new FEM schemes (rectangular elements), in which components are best elements of the minimum conditions given appropriate functional boundary value problems. The results of the thesis were partly used within the state budget theme and introduced into some academic courses at UIPA. Uses - engineering, power engineering.