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dc.contributor.advisor Temam, Roger en Jung, Chang-Yeol en 2010-06-01T22:02:08Z en 2027-02-01T23:02:08Z en 2010-06-16T20:31:19Z 2010-06-01T22:02:08Z en 2006 en
dc.identifier.uri en
dc.description Thesis (PhD) - Indiana University, Mathematics, 2006 en
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
dc.language.iso EN en
dc.publisher [Bloomington, Ind.] : Indiana University en
dc.rights This work is licensed under the Creative Commons Attribution 3.0 Unported License. en
dc.rights.uri en
dc.subject convection diffusion equation en
dc.subject boundary layer en
dc.subject stability analysis en
dc.subject singularly perturbed problem en
dc.subject.classification Mathematics en
dc.title Numerical Approximation of two dimensional Singularly Perturbed Problems en
dc.type Doctoral Dissertation en

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