Adaptive discontinuous galerkin methods for non-linear reactive flows

Uzunca, Murat
The aim of this thesis is to solve the convection/reaction dominated non-stationary semi-linear diffusion-convection-reaction problems with internal/boundary layers in an accurate and efficient way using a time-space adaptive algorithm. We use for space discretization the symmetric interior penalty discontinuous Galerkin method, and backward Euler for time discretization. Our main interest is to derive robust residual-based a posteriori error estimators both in space and time. To derive the a posteriori bounds for the fully discrete system, we utilize the elliptic reconstruction technique. The use of elliptic reconstruction technique allows us to use the a posteriori error estimators derived for stationary models and to obtain optimal orders in $L^{\infty}(L^2)$ norms.


Adaptive discontinuous Galerkin methods for convection dominated optimal control problems
Yücel, Hamdullah; Karasözen, Bülent; Department of Scientific Computing (2012)
Many real-life applications such as the shape optimization of technological devices, the identification of parameters in environmental processes and flow control problems lead to optimization problems governed by systems of convection di usion partial di erential equations (PDEs). When convection dominates di usion, the solutions of these PDEs typically exhibit layers on small regions where the solution has large gradients. Hence, it requires special numerical techniques, which take into account the structu...
Generalized finitedifference method in elastodynamics using perfectly matched layer
Korkut, Fuat; Tokdemir, Turgut; Department of Engineering Sciences (2012)
This study deals with the use of the generalized finite difference method (GFDM) in perfectly matched layer (PML) analysis of the problems in wave mechanics, in particular, in elastodynamics. It is known that PML plays the role of an absorbing layer, for an unbounded domain, eliminating reflections of waves for all directions of incidence and frequencies. The study is initiated for purpose of detecting any possible advantages of using GFDM in PML analysis: GFDM is a meshless method suitable for any geometry...
BENNER, Peter; Yücel, Hamdullah (2017-01-01)
We investigate an a posteriori error analysis of adaptive finite element approximations of linear-quadratic boundary optimal control problems under bilateral box constraints, which act on a Neumann boundary control. We use a symmetric interior Galerkin method as discretization technique. An efficient and reliable residual-type error estimator is introduced by invoking data oscillations. We then derive local upper and lower a posteriori error estimates for the boundary control problem. Adaptive mesh refineme...
Fully computable convergence analysis of discontinous Galerkin finite element approximation with an arbitrary number of levels of hanging nodes
Özışık, Sevtap; Kaya Merdan, Songül; Riviere, Beatrice M.; Department of Mathematics (2012)
In this thesis, we analyze an adaptive discontinuous finite element method for symmetric second order linear elliptic operators. Moreover, we obtain a fully computable convergence analysis on the broken energy seminorm in first order symmetric interior penalty discontin- uous Galerkin finite element approximations of this problem. The method is formulated on nonconforming meshes made of triangular elements with first order polynomial in two di- mension. We use an estimator which is completely free of unknow...
Adaptive Symmetric Interior Penalty Galerkin (SIPG) method for optimal control of convection diffusion equations with control constraints
Yücel, Hamdullah; Karasözen, Bülent (2014-01-02)
In this paper, we study a posteriori error estimates of the upwind symmetric interior penalty Galerkin (SIPG) method for the control constrained optimal control problems governed by linear diffusion-convection-reaction partial differential equations. Residual based error estimators are used for the state, the adjoint and the control. An adaptive mesh refinement indicated by a posteriori error estimates is applied. Numerical examples are presented for convection dominated problems to illustrate the theoretic...
Citation Formats
M. Uzunca, “Adaptive discontinuous galerkin methods for non-linear reactive flows,” Ph.D. - Doctoral Program, Middle East Technical University, 2014.