### On finite-element approximation of functions in a plain domain with curvilinear boundary

Title On finite-element approximation of functions in a plain domain with curvilinear boundary I. V. Zakharova11Tver State University The problem of approximation of a function of two variables defined in a curvilinear trapezoid by the finite element method is investigated in the article. In this domain а partition of unity is constructed which is subordinate to some covering. Inside every covering set the function of interest is approximated by polynomials in $L_{2}$ space. The criterion for the approximation quality is the relative error calculated with respect to norm in $L_{2}$. The elucidation of function approximation efficiency is necessary for finding the limits of applicability of the finite element method for the numerical solution of mathematical physics' problems. The set of programs has been developed in MATLAB environment that implements the algorithm for approximation of functions by finite element method. Examples are given demonstrating the working capacity of the software package. finite element method, approximation of functions Zakharova I. V. ''On finite-element approximation of functions in a plain domain with curvilinear boundary'' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 284-292. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper39.pdf. - Date of access: 24.08.2019.