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dc.contributor.advisor Temam, Roger en_US
dc.contributor.author Jung, Chang-Yeol en_US
dc.date.accessioned 2010-06-01T22:02:08Z
dc.date.available 2027-02-01T23:02:08Z
dc.date.available 2010-06-16T20:31:19Z
dc.date.issued 2010-06-01T22:02:08Z
dc.date.submitted 2006 en_US
dc.identifier.uri http://hdl.handle.net/2022/7651
dc.description Thesis (PhD) - Indiana University, Mathematics, 2006 en_US
dc.description.abstract We demonstrate how one can improve the numerical solution of singularly perturbed problems involving multiple boundary layers by using a combination of analytic and numerical tools. Incorporating the so-called boundary layer elements (BLE), which absorb the singularities due to the boundary layers, into finite element spaces can improve the accuracy of approximate solutions and result in significant simplifications. We discuss here convection-diffusion equations in the case where both ordinary and parabolic boundary layers are present. We also revise the BLE so that it has a small compact support and hence the resulting linear system becomes sparse, more precisely, block tridiagonal. We prove the validity of the revised element for some singularly perturbed convection-diffusion equations via numerical simulations and via the H^1- approximation error analysis. Furthermore due to the compact structure of the BLE we are able to prove the L^2- stability analysis of the scheme and derive the L^2- error approximations. en_US
dc.language.iso EN en_US
dc.publisher [Bloomington, Ind.] : Indiana University en_US
dc.rights This work is licensed under the Creative Commons Attribution 3.0 Unported License. en
dc.rights.uri http://creativecommons.org/licenses/by/3.0/ en
dc.subject convection diffusion equation en_US
dc.subject boundary layer en_US
dc.subject stability analysis en_US
dc.subject singularly perturbed problem en_US
dc.subject.classification Mathematics en_US
dc.title Numerical Approximation of two dimensional Singularly Perturbed Problems en_US
dc.type Doctoral Dissertation en_US


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This work is licensed under the Creative Commons Attribution 3.0 Unported License. This work is licensed under the Creative Commons Attribution 3.0 Unported License.

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