A posteriori estimation of the error in the finite element solution by computation of the guaranteed upper and lower bounds /
This dissertation addresses reliable finite element analysis of boundary value problems in engineering computations, where the solution quantities which are of interest to the engineer will be computed together with an estimate of their error. The solution quantities often computed during design and...
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
1999.
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| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=730319031&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | This dissertation addresses reliable finite element analysis of boundary value problems in engineering computations, where the solution quantities which are of interest to the engineer will be computed together with an estimate of their error. The solution quantities often computed during design and certification phases are the temperature/displacement, flux/stress in a region, flux/stress intensity factor at the crack tip or corner, reaction at a fixed end, etc. The existing finite element analysis software concentrate primarily on obtaining a solution rapidly and do not guarantee the accuracy of these solution quantities. Recent developments in error- estimation and adaptive mesh refinement strategies leave led to new algorithms to compute solution quantities of interest within the prescribed tolerance. The drawback of these algorithms is that the quality of the estimate of the error in the solution quantities is not guaranteed, i.e., the estimated error could be greater or smaller than the exact error. Therefore, we have developed a new method of estimation of the error in the quantities of interest - computation of guaranteed upper and lower bounds for the errors in the quantities of interest. The guaranteed upper and lower bounds for the errors in the quantities of interest are based on the capability to compute bounds for the energy norm of the error. The tools for computation of bounds for the energy norm of the error are the solutions of the local residual problems, which are often implemented in finite element programs which have a posteriori error estimation capabilities. The main features of the upper and lower bounds given in this dissertation are - (1) The upper and lower bounds are guaranteed for the exact error in the quantities of interest, unlike the bounds proposed in recent literature which are guaranteed only for the energy norm of the error with respect to an enriched (truth-mesh) finite element solution; (2) The sharpness of the bounds can be further improved by employing a few iterations of a relatively inexpensive iterative scheme. We conclude this dissertation with a comparison of the past work on error-estimation with the current approach. |
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| Item Description: | Vita. "Major Subject: Aerospace Engineering". |
| Physical Description: | xx, 203 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilm Inc. |
| Bibliography: | Includes bibliographical references (leaves 173-179). |