%0 Journal Article
%A Siryk, Sergey V.
%A Salnikov, Nikolay N.
%A Tereshchenko, Igor A.
%D 2010
%I Begell House
%K construction of piecewise-polynomial weighting functions, Petrovâ€“Galerkin method, two-dimensional domain, finite number of variable parameters, construction of finite-dimensional model, nonstationary process, convection-diffusion, arbitrary domain, ordinary differential
%N 6
%P 67-83
%R 10.1615/JAutomatInfScien.v42.i6.50
%T On Construction of Finite-Dimensional Mathematical Model of Convection−Diffusion Process with Usage of the Petrov−Galerkin Method
%U http://dl.begellhouse.com/journals/2b6239406278e43e,7c17eac404c33891,00642f3b10f058cf.html
%V 42
%X We proposed technique of construction of piecewise-polynomial weighting functions for the Petrov−Galerkin method in two-dimensional domain. The form of these functions is defined by finite number of variable parameters, connected with grid edges. We consider several variants of selection of these parameters depending on the modulus and direction of the vector of advection rate. The method of construction of finite-dimensional model of nonstationary process of convection-diffusion for arbitrary domain in the form of system of ordinary differential equations was proposed. Accuracy of the obtained model is ascertained by comparison of numerical and analytical solutions of a testing problem.
%8 2010-07-06