A qualitative accuracy consideration on arch elements

In the present paper, discretization errors in the finite element analysis of arches are investigated quantitatively. So far they have been estimated as an order, such as a power of the element size by means of functional analysis; however, it is insufficient for practical applications, because they depend to a great extent upon the constant of proportionality, which is investigated herein. As a result, it is shown that the constant is affected largely by the arch's stiffness. Errors for displacements are also evaluated with the aid of the energy principle. A formula for a posteriori estimating errors is proposed, which can be evaluated only from the finite element solutions calculated. The validity of the present theory is verified by numerical examples.