SEVEN-POINT FINITE ELEMENT OF INTEGRAL TYPE APPLIED TO CONFORMING - NONCONFORMING METHOD

Abstract

The paper deals with integral variants of a seven-point triangular finiteelement. This is an enriched quadratic element constructed by adding a non-negativebasis bulb-function which vanishes on the element boundary. The polynomial spacewhich seven-point element uses is P 2 + span{x 2 y + xy 2 }. The main goal here is to determine two-sided bounds of eigenvalues for a second-order elliptic operator. The method consists of finite element solving of the problemby means of seven-point conforming element and then constructing an nonconforminginterpolant of the approximate conforming eigendunctions. Thus, solving only oncethe eigenvalue problem, we get upper and lower bounds for the exact eigenvalues.Furthermore, the fact that the nonconforming interpolants uses the nodal values of theconforming approximate eigenfunctions gives an obvious computational advantage.Finally, numerical experiments confirming the efficiency of the proposed algorithmare also provided.