ESTIMATED ERROR-BOUNDS FOR FINITE-ELEMENT SOLUTIONS OF ELLIPTIC BOUNDARY-VALUE-PROBLEMS

A new error estimate is introduced which adds to the theory of error b ounds. First, the statically (SAS) and kinematically admissible fields (KAS), are studied. Then, the theory of error bounds using these fiel ds is presented. Due to the inherent complexities involved in the dete rmination of statically admissible stress field (SAS), a quasi-statica lly admissible stress (quasi-SAS) held is used instead, and a so-calle d error measure, the estimated error bound, is defined. This error mea sure is determined by the sum of two terms, one of which is expressed by the normalized energy norm of the distance between the KAS field, c omputed by the displacement finite element method, to a quasi-SAS fiel d. The other term is the error, in normalized energy norm, due to the application of quasi-SAS field instead of the statically admissible fi eld. Because this term is also difficult to compute, an upper bound fo r this error is derived. In addition, some approximate expressions for this term are computed. The summation of the two terms comprises the estimated error bound. To show the effectiveness of this error measure , it is calculated for some test problems and compared with the exact errors in the solutions, when they exist.