Nosov K. Finite Element Method with coordinate functions selection under modelling of physics processes.

The object of study: methods of an approximate solution of boundary value problems of mathematical physics. The purpose of study is investigation of properties of the FEM with coordinate functions selection and research of iterative algorithm which are used for construction FE-bases for the chosen boundary value problems. The methods: the theory of the differential equations and their systems, a calculus of variations and variational methods of nonlinear operators, elements of differential calculus in normed spaces, methods of a functional analysis. Novelty: properties of schemas of a finite element method with coordinate functions selection in application to the chosen modelling problems are investigated. The theoretical value of work: correctness of the offered iteration schema «flip-flop» constructions of an approximate solution by a finite element method with coordinate functions selection is proved; for each step of algorithm «flip-flop» the a posteriori estimation of value which characterizes a reduce of square of a error in energy norm is gained. The practical value of work: precision algorithms of an approximate solution of actual problems of mathematical physics which concern to a potential theory and theory of elasticity are developed. Degree of the introduction: results of work is introduced on SV «Malyshev Plant» according to economic contract 24943. Efficiency of the introduction: high. The sphere of the use: design offices, research units the NAS of Ukraine, high educational institution. Key words: Poisson’s equation, biharmonic equation, Finite Element Method, symmetric-boundary problem, coordinate functions, a posteriori estimates.