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dc.contributor.advisorEfendiev, Yalchin
dc.creatorJiang, Lijian
dc.date.accessioned2010-01-15T00:08:21Z
dc.date.accessioned2010-01-16T01:10:43Z
dc.date.available2010-01-15T00:08:21Z
dc.date.available2010-01-16T01:10:43Z
dc.date.created2008-08
dc.date.issued2009-05-15
dc.identifier.urihttps://hdl.handle.net/1969.1/ETD-TAMU-2991
dc.description.abstractIn this dissertation we develop, analyze and implement effective numerical methods for multiscale phenomena arising from flows in heterogeneous porous media. The main purpose is to develop innovative numerical and analytical methods that can capture the effect of small scales on the large scales without resolving the small scale details on a coarse computational grid. This research activity is strongly motivated by many important practical applications arising in contaminant transport in heterogeneous porous media, oil reservoir simulations and subsurface characterization. In the work, we investigate three main multiscale numerical methods, i.e., multiscale finite element method, partition of unity method and mixed multiscale finite element method. These methods employ limited single or multiple global information. We apply these numerical methods to partial differential equations (elliptic, parabolic and wave equations) with continuum scales. To compute the solution of partial differential equations on a coarse grid, we define global fields such that the solution smoothly depends on these fields. The global fields typically contain non-local information required for achieving a convergence independent of small scales. We present a rigorous analysis and show that the proposed global multiscale numerical methods converge independent of small scales. In particular, a global mixed multiscale finite element method is extensively studied and applied to two-phase flows. We present some numerical results for two-phase simulations on coarse grids. The numerical results demonstrate that the global multiscale numerical methods achieve high accuracy.en
dc.format.mediumelectronicen
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.subjectMultiscale Finite Element Methodsen
dc.subjectPartial Differential Equationsen
dc.titleMultiscale numerical methods for partial differential equations using limited global information and their applicationsen
dc.typeBooken
dc.typeThesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorTexas A&M Universityen
thesis.degree.nameDoctor of Philosophyen
thesis.degree.levelDoctoralen
dc.contributor.committeeMemberLazarov, Raytcho
dc.contributor.committeeMemberMohanty, Binayak
dc.contributor.committeeMemberWalton, Jay
dc.type.genreElectronic Dissertationen
dc.type.materialtexten
dc.format.digitalOriginborn digitalen


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