Scientific publications of the Ivan Franko National University of Lviv

Visnyk of the Lviv University. Series Applied Mathematics and Computer Science

Additional information
Year 2002
Volume 5
Authors Shynkarenko G., Kozarevska Y.
Name of the article The Regularization of numerical solutions of variational problems of impurities migration: an adaptive finite element method. Part 1
Abstract A posteriori error estimations of the finite element method (FEM) approximations of substance stationary convection-diffusion-response problems in an incompressible continuum have been constructed on the basis of mass conservation equation. The functional of error source, partly defined by the residual of the equation above each finite element of decomposition, and the variation problem for the finding of FEM approximation error lay in the basis of the analysis. The approximate solutions of this problem in bubble-function spaces have allowed us to construct low-budget and convenient error estimators of dot and integrated performances in natural for this class of problems norms with particular properties: 1. They define the association of an error level on a finite element from its geometrical performances, Peclet and Struhal similitude parameters and the mass of unstable impurity. 2. They create a reliable basis for the optimum adaptation of calculated grids that are capable to map a required solution structure with beforehand given precision. The error estimators constructing technique has been demonstrated on the example of one- and two-dimensional migration problems where the approximate solution was built on the base of finite linear functions.
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