Some effects of system idealizations, singularities and mesh patterns on finite element solutions

Abstract

Solution accuracy, convergence, and rate of convergence are of paramount importance in finite element analysis. Important variables affecting the solution, in addition to the particular finite element utilized are structural idealizations, singularities and mesh pattern. These are the variables considered in this article. Numerical examples are considered to demonstrate some of the effects of these variables on the solution convergence. The example problems indicate monotonie upper or lower bound solution convergence for conforming elements in the proper n- sequence when idealization and discretization errors are of the same sign. For singularity cases, solution convergence is usually well behaved for practical n values, but at a reduced rate of convergence. Various mesh patterns did affect solution accuracy, but did not affect convergence or convergence rate.