Practical aspects of a-posteriori estimation for reliable finite element analysis
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In this paper we study the problem of a-posteriori estimation of the error in the derivatives, strains and stresses in finite element solutions of the elasticity problem. Given any small patch of elements, we split the error in the patch into two components: the local (or near-field) error which is the response of the elastic continuum in the patch when the domain is loaded only by the near-field residuals, i.e. the residuals of the finite element solution in the elements in the neighborhood of the patch (the patch and a few, e.g. one, surrounding mesh-layers), and the pollution (or far-field) error which is the response in the patch when the domain is loaded by the residuals of the finite element solution in the elements outside the neighborhood of the patch (the far-field residuals). The local error can be estimated by employing element error indicators, which are determined using local computations in the neighborhood of the patch (element residual problems, or local averagings), while the estimation of the pollution error requires a global extraction. This extraction can be based on the ability of the code to compute energy inner products of error indicator functions corresponding to the finite element solution and finite element approximations of a few auxiliary functions which are determined (with negligible cost when a direct solver is employed) by solving the global finite element equations for a few additional auxiliary loads. 1998 Elsevier Science Ltd. All rights reserved.
