Computer-based analysis of error estimation and superconvergence in finite element computations /
In this study we partition the error in the finite element solution into the local and the global (pollution) components. A completely computer-based procedure is developed to construct the asymptotic finite element solution for the h-version of the finite element method, for mesh-patches in the in...
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
1997.
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| Subjects: | |
| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=739891821&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | In this study we partition the error in the finite element solution into the local and the global (pollution) components. A completely computer-based procedure is developed to construct the asymptotic finite element solution for the h-version of the finite element method, for mesh-patches in the interior of the domain and at the boundary. This asymptotic finite element solution is then employed to design a computer-based approach for determining the asymptotic bounds of a-posteriori estimators for the local error. Several existing error estimators have been analysed and ranked according to their asymptotic reliability with respect to the local mesh geometry, material properties and the class of solutions of interest. The computer-based approach is extended to analyze the superconvergence properties of the finite element solution, and several local averagings which employ the local finite element solution. The more robust concept of q%-superconvergence is also introduced, in contrast to the classical definition of superconvergence. Based on the analyses of the error estimators and local averagings, several improvements have been proposed and studied extensively in this study. It has been systematically demonstrated that the proposed improvements can be expected to be superior to the existing error estimators and local averagings, in general. We also present a comprehensive analysis of the pollution error. Based on this analysis, an a-posteriori estimator for the pollution error is developed and studied. Further, this estimator is employed to design a new adaptive algorithm for the control of the pollution error in a desired patch of elements. It is shown that this adaptive algorithm achieves the desired accuracy of the solution quantities, in the patch of interest, with significantly lesser computational effort, when compared to the conventional adaptive algorithms. |
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| Item Description: | Vita. "Major Subject: Aerospace Engineering". |
| Physical Description: | xx, 291 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references: pages 274-282. |