Estimating the manipulation errors in finite element analysis, Part I

In Part I of this two-part work, the relative errors in representing and processing real numbers in digital computers are reviewed, and the computation of the digits lost from the relative errors is shown. The upper bound estimate of the relative error in the solution of Kξ = p for the displacements ξ is given as a function of the condition number of the stiffness matrix K, and the relative errors in K and the load vector p. The computation of relative errors for p and K by equilibrium checks is outlined, and various estimates for the condition number of the stiffness matrix are given.