Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8814Research ArticleBoundary Method of Weighted Residuals with Discontinuous Basis Functions for High-Accuracy Solving Linear Boundary Value Problems with Laplace and Poisson’s EquationYuldashevO ILaboratory of Information Technologiesyuldash@cv.jinr.ruYuldashevaM BLaboratory of Information Technologiesjuldash@cv.jinr.ruJoint Institute of Nuclear Research15042013414315308092016Copyright © 2013,2013In the present paper the method of least squares with T-elements for solving linear boundary value problems with Laplace and Poisson’s equations is developed. In this approach it is oﬀered to use discontinuous basis functions of a high-order approximation from special functional spaces, elaborated by the authors earlier. Advantage of the algorithm in comparison with Galerkin’s standard method is that, in the process of adaptive solving, it makes possible to condense economically a mesh and, moreover, to use diﬀerent order of approximation of the solution on each cell of partition of calculated region. In contrast to Galerkin’s method with discontinuous basis functions, a penalty parameter here is not required, and the matrix of a discretized problem also is symmetric and positively deﬁnite. Examples of calculations by means of the schemes providing computer accuracy of the solution of boundary value problems for polynomials up to seventh order inclusive are given. In a three-dimensional case h − p-convergence of approximate solution to the exact one is shown.boundary method of weighted residualsdiscontinuous basis functionsT-elementshigh accuracyLaplace’s equationPoisson’s equationграничный метод взвешенных невязокразрывные базисные функцииТ-элементывысокая точностьуравнение Лапласауравнение Пуассона