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

*(English)*Zbl 0946.74057From the summary: The general procedure developed by T. M. Shih [Int. J. Numer. Methods Eng. 21, 1027-1037 (1985; Zbl 0566.68034)] 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. The procedure is illustrated using two-dimensional stress analysis and transient heat conduction problems.

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74B10 | Linear elasticity with initial stresses |

80A20 | Heat and mass transfer, heat flow (MSC2010) |

##### Keywords:

code verification; error elimination; debugging; forced boundary conditions; volume weighted residuals; weighted boundary residuals; natural boundary conditions; two-dimensional stress analysis; transient heat conduction
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\textit{D. A. Blank} and \textit{J. Loui P.}, Int. J. Numer. Methods Eng. 44, No. 9, 1187--1204 (1999; Zbl 0946.74057)

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