A-posteriori estimation and adaptive control of the error in the solution quantity of interest

Due to the character of the original source materials and the nature of batch digitization, quality control issues may be present in this document. Please report any quality issues you encounter to digital@library.tamu.edu, referencing the URI of the item.Includes bibliographical references: p. 101-103.Issued also on microfiche from Lange Micrographics.The engineers are primarily interested in quantities like stresses and displacements in the critical regions, the stress intensity factor at the crack-tip of an initiated crack, etc., and the error in these quantities. The majority of the existing adaptive finite element codes employ a-posteriori estimation and adaptivity with respect to the global energy norm, and cannot optimize the approximation with respect to engineering goals. In this thesis, we address the problem of the a-posteriori estimation and adaptive control of the error in the quantity of interest. The major tool for the estimation of the error in the desired quantity is the splitting of the error into two components: the near-field or local error, and the far-field or pollution error. The local component of the error is estimated by the local error indicators, while the estimation of the pollution error is based on a global extraction. This approach leads to accurate estimates in the quantity of interest, for complex domains and coarse meshes of the type used in engineering computations. In this thesis, we considered finite element approximations on meshes of curvilinear quadrilaterals obtained from an initial coarse mesh of superelements, because such meshes are often used in practical computations. We also gave various examples of adaptive strategies based on the idea of controlling the error in the solution quantity of interest (e.g., the stress at a point, the stress intensity factor, etc.). This approach provides direct control of the error in the desired quantity and is more economical than the adaptive strategies which control the error in the global energy norm