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

The general procedure developed by Shih for eliminating computer coding errors has been both simpli ed for nite element applications and extended for use in the veri cation 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 nite 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 modi cation can make possible the implementation of Shihʹs general procedure into existing nite element codes without having to carry out any additional discretization steps. The employment of this modi ed procedure is illustrated using two-dimensional (2-D) stress analysis and transient heat conduction problems. Copyright