Stabilized finite element methods for time dependent convection-diffusion equations için kapak resmi
Stabilized finite element methods for time dependent convection-diffusion equations
Baysal, Onur.
Yazar Ek Girişi:
Yayın Bilgileri:
[s.l.]: [s.n.], 2012.
Fiziksel Tanımlama:
x, 96 leaves.: ill. + 1 computer laser optical disc.
In this thesis, enriched finite element methods are presented for both steady and unsteady convection diffusion equations. For the unsteady case, we follow the method of lines approach that consists of first discretizing in space and then use some time integrator to solve the resulting system of ordinary differential equation. Discretization in time is performed by the generalized Euler finite difference scheme, while for the space discretization the streamline upwind Petrov-Galerkin (SUPG), the Residual free bubble (RFB), the more recent multiscale (MS) and specific combination of RFB with MS (MIX) methods are considered. To apply the RFB and the MS methods, the steady local problem, which is as complicated as the original steady equation, should be solved in each element. That requirement makes these methods quite expensive especially for two dimensional problems. In order to overcome that drawback the pseudo approximation techniques, which employ only a few nodes in each element, are used. Next, for the unsteady problem a proper adaptation recipe, including these approximations combined with the generalized Euler time discretization, is described. For piecewise linear finite element discretization on triangular grid, the SUPG method is used. Then we derive an efficient stability parameter by examining the relation of the RFB and the SUPG methods. Stability and convergence analysis of the SUPG method applied to the unsteady problem is obtained by extending the Burman’s analysis techniques for the pure convection problem. We also suggest a novel operator splitting strategy for the transport equations with nonlinear reaction term. As a result two subproblems are obtained. One of which we may apply using the SUPG stabilization while the other equation can be solved analytically. Lastly, numerical experiments are presented to illustrate the good performance of the method.
Yazar Ek Girişi:
Tek Biçim Eser Adı:
Thesis (Doctoral)--İzmir Institute of Technology: Mathematics.

İzmir Institute of Technology: Mathematics--Thesis (Doctoral).
Elektronik Erişim:
Access to Electronic Versiyon.


Materyal Türü
Demirbaş Numarası
Yer Numarası
Durumu/İade Tarihi
Tez T001035 QA377 .B36 2012

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