Pointwise extensions to the Zienkiewicz-Zhu adaptive refinement procedure

The refinement guide and error estimator of the Zienkiewicz and Zhu (ZZ) adaptive refinement procedure for upgrading finite element models are improved in this work. A new approach for identifying the improvements needed to produce a more accurate finite element model, based on determining the in situ modeling deficiencies contained in the individual elements, is developed. The point-wise error estimator developed here is based on the inter-element jumps at the nodes in the finite element strain representation. It is simpler to compute and is expressed in terms of quantities central to solid mechanics. This work also shows that the smoothed solution, central to the ZZ approach, is an improved solution because it adds a portion of the discretization errors, which are identical to the residuals produced by the failure of the finite element solution to satisfy the governing differential equation being solved, to the existing finite element solution.