PROGNOSTIC ESTIMATION OF APPROXIMATIVE PROPERTIES OF BASES FOR TRIANGULAR FINITE ELEMENTS OF II ORDER
Journal Title: Вісник Кременчуцького національного університету імені Михайла Остроградського - Year 2015, Vol 95, Issue 6
Abstract
Purpose. The aim is to build and rationale for the practical application of basic functions in a power series for the finite element of the second order in the form of an isosceles right triangle. Methodology. For prognostic evaluation of the proposed basis functions approximationary properties we have used the value of the trace of stiffness (thermal conductivity) matrix of the element and the condition number of the Gram matrix for the functions of the test basis. Results. For the finite element of the second order in the form of an isosceles right triangle new base is constructed. On test problems it leads to solutions of higher accuracy compared with known bases. It is shown that local characteristics such as the value of the trace of stiffness (thermal conductivity) matrix of the element and the condition number of the Gram matrix for the basis functions are not consistent and not uniquely determined basis with the best approximationary properties. Originality. The relationships between the coefficients of power series, which describe the basic functions of the test finite element, and its local characteristics are established for the first time. On the graphs of these dependencies the placement features of points that correspond to known bases of test finite element and the authors' proposal basis are studied. Practical value. Modified bases are tested when solving the practical problems. The accuracy of the solutions is estimated. Recommendations on the feasibility of practical use of bases studied in the article are made. References 10, tables 1, figures 4. Keywords: triangular finite element, local estimates.
Authors and Affiliations
Galina Tuluchenko, Nataliya Starun, Tatiana Belousova, Stanislav Bezerdyan
Keywords
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