A coding error elimination procedure for verifying finite element programs with forced and natural boundary conditions

Abstract

The general procedure developed by Shih for eliminating computer coding errors has been both simplified for finite element applications and extended for use in the verification of the coding of forced and natural boundary conditions. To accomplish these two objectives simultaneously, use is made of volume weighted residuals for all elements within the solution regime and of area weighted boundary residuals for all elements having natural boundary conditions on one or more of their borders. This procedure can thus be used to verify finite element codes with a combination of both forced (Dirichlet) and natural (Neumann and Robbins) boundary conditions. Depending on the equations being solved and the boundary conditions they are being subjected to, this modification can make possible the implementation of Shih's general procedure into existing finite element codes without having to carry out any additional discretization steps. The employment of this modified procedure is illustrated using two-dimensional (2-D) stress analysis and transient heat conduction problems. Copyright © 1999 John Wiley & Sons, Ltd.