On discretization and iterative techniques for second-order problems with applications to multiphase flow in porous media /
There are three related topics which are considered in this
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| Format: | Thesis Book |
| Language: | English |
| Published: |
[Place of publication not identified] :
[publisher not identified] ;
1996.
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| Subjects: | |
| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=743267461&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | There are three related topics which are considered in this dissertation: the discretization of second-order partial differential equations (PDEs), the development of new iterative techniques for solving the resulting systems of equations efficiently, and applications of this theory to the important problem of modeling multiphase fluid flow in porous media. New fully discrete finite element schemes of backward Euler type which utilize local refinement in time and space are constructed and analyzed. It is shown that these schemes are unconditionally stable and an error analysis in maximum norms is provided. New inexact nonoverlapping domain decomposition preconditioners, applied to the solution of problems arising from Galerkin, mixed, and locally refined finite element discretizations of second-order PDES, are constructed and analyzed. The preconditioners are developed based only on the assumption that the interior solves are provided by uniform preconditioning forms. They exhibit the same asymptotic condition number growth as corresponding exact preconditioners but are much more efficient computationally. In addition, their preconditioning effect is independent of jumps of the operator coefficients across subdomain boundaries. An abstract analysis of inexact variants of the classical Uzawa iterative algorithm for solving saddle-point problems is developed. Both linear and nonlinear inexact algorithms are analyzed and special considerations for second-order PDEs are provided. Applications of the developed new discretizations and iterative algorithms to problems of fluid flow in porous media are considered. Emphasis is given to the two-phase fractional flow model in the context of a class of environmental applications. Illustrative numerical examples involving the new techniques developed as well as a computer simulation of groundwater flow and contaminant transport are included. |
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| Item Description: | Vita. "Major Subject: Mathematics". |
| Physical Description: | xii, 160 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references. |